[Bug]: TOOL_CALL_START handler in defaultApplyEvents is not idempotent — duplicates toolCalls when connect() replays historic events over pre-populated message state`

### Pre-flight Checklist

- [x] I have searched [existing issues](https://github.com/ag-ui-protocol/ag-ui/issues) and this hasn't been reported yet.
- [x] I am using the **latest** version AG-UI.

### Describe the Bug

In `defaultApplyEvents` (`sdks/typescript/packages/client/src/apply/default.ts`), the `TOOL_CALL_START` case unconditionally pushes a new entry into `targetMessage.toolCalls` with no duplicate guard:

```ts
targetMessage.toolCalls ??= [];
targetMessage.toolCalls.push({
// ← no idempotency check
id: toolCallId,
type: "function",
function: { name: toolCallName, arguments: "" },
});
```

This is safe for a fresh run, but breaks when `connectAgent()` is called on an agent whose `messages` state already contains a completed assistant message with tool calls (e.g. after a prior run). The `connect()` endpoint replays compacted historic events — including `TOOL_CALL_START` for tool calls that are already present in the initial message state. Because `defaultApplyEvents` does not check for an existing entry before pushing, the same tool call ID is inserted twice:

```ts
message.toolCalls = [
{ id: "call_abc123", ... }, // ← already in initial state
{ id: "call_abc123", ... }, // ← pushed again by replayed TOOL_CALL_START
]
```

Consumers that use `toolCall.id` as a React key (e.g. CopilotKit's `CopilotChatToolCallsView`) then produce a React duplicate-key warning, and React may render the tool call twice or omit it.

### Steps to Reproduce

1. Use `@ag-ui/client` with a runtime that supports `connect()` (e.g. CopilotKit's `InMemoryAgentRunner`)
2. Register a frontend tool via `useFrontendTool` (or any tool the agent can call)
3. Send a message that triggers a tool call and let the run complete
4. Trigger a reconnect — e.g. reload the page, or call `connectAgent()` on an agent whose `messages` already contain the completed assistant message
5. Observe the browser console

The sequence that triggers the bug:

```ts
// Initial agent message state (from prior run):
// messages = [{ id: "msg_1", role: "assistant", toolCalls: [{ id: "call_abc" }] }]

// connect() replays compacted historic events:
TOOL_CALL_START { toolCallId: "call_abc", parentMessageId: "msg_1" } ← pushed again
TOOL_CALL_ARGS { toolCallId: "call_abc", delta: '{"location":"NYC"}' }
TOOL_CALL_END { toolCallId: "call_abc" }

// Result:
// msg_1.toolCalls = [{ id: "call_abc" }, { id: "call_abc" }] ← duplicate
```

Note: `InMemoryAgentRunner.connect()` does filter already-seen events for text messages (via a `messageId`-keyed set), but this guard only checks for the `messageId` property — `TOOL_CALL_START` carries `toolCallId`, so it is not filtered and always passes through.

### Expected Behavior

Processing a `TOOL_CALL_START` event for a `toolCallId` that already exists in `targetMessage.toolCalls` should be a no-op. `defaultApplyEvents` must be idempotent with respect to tool call IDs, since `connect()` legitimately replays the same historic events over an agent that already has them in its message state.

**Proposed fix** — a one-liner guard before the push:

```ts
targetMessage.toolCalls ??= [];
if (!targetMessage.toolCalls.some((tc) => tc.id === toolCallId)) {
targetMessage.toolCalls.push({
id: toolCallId,
type: "function",
function: { name: toolCallName, arguments: "" },
});
}
```

### Environment

```text
- AG-UI package(s) & version(s): `@ag-ui/client@0.0.52`, `@ag-ui/core@0.0.52`
- Runtime: Node.js v24.14.1
- Consumer: `@copilotkit/react-core@1.55.3` with `InMemoryAgentRunner`
```

### Screenshots

_No response_

### Logs & Errors

```shell
Encountered two children with the same key, `call_uUF5OZtugHE6tyoC9PPtpAs6`.
Keys should be unique so that components maintain their identity across updates.
Non-unique keys may cause children to be duplicated and/or omitted —
the behavior is unsupported and could change in a future version.
at CopilotChatToolCallsView
at MemoizedSlotWrapper
at CopilotChatAssistantMessage
...

Full Stack Trace

installHook.js:1 Encountered two children with the same key, `call_6L4zojIwnOpVsBXCwFmVvCMp`. Keys should be unique so that components maintain their identity across updates. Non-unique keys may cause children to be duplicated and/or omitted — the behavior is unsupported and could change in a future version.

overrideMethod @ installHook.js:1

(anonymous) @ react-dom-client.development.js:6604

runWithFiberInDEV @ react-dom-client.development.js:871

warnOnInvalidKey @ react-dom-client.development.js:6603

reconcileChildrenArray @ react-dom-client.development.js:6672

reconcileChildFibersImpl @ react-dom-client.development.js:6993

(anonymous) @ react-dom-client.development.js:7098

reconcileChildren @ react-dom-client.development.js:9701

updateFunctionComponent @ react-dom-client.development.js:10182

beginWork @ react-dom-client.development.js:11778

runWithFiberInDEV @ react-dom-client.development.js:871

performUnitOfWork @ react-dom-client.development.js:17641

workLoopSync @ react-dom-client.development.js:17469

renderRootSync @ react-dom-client.development.js:17450

performWorkOnRoot @ react-dom-client.development.js:16504

performWorkOnRootViaSchedulerTask @ react-dom-client.development.js:18957

performWorkUntilDeadline @ scheduler.development.js:45

<>

(anonymous) @ react-jsx-runtime.development.js:335

(anonymous) @ copilotkit-Cd-NrDyp.mjs:4795

CopilotChatToolCallsView @ copilotkit-Cd-NrDyp.mjs:4793

react_stack_bottom_frame @ react-dom-client.development.js:25904

renderWithHooks @ react-dom-client.development.js:7662

updateFunctionComponent @ react-dom-client.development.js:10166

beginWork @ react-dom-client.development.js:11778

runWithFiberInDEV @ react-dom-client.development.js:871

performUnitOfWork @ react-dom-client.development.js:17641

workLoopSync @ react-dom-client.development.js:17469

renderRootSync @ react-dom-client.development.js:17450

performWorkOnRoot @ react-dom-client.development.js:16504

performWorkOnRootViaSchedulerTask @ react-dom-client.development.js:18957

performWorkUntilDeadline @ scheduler.development.js:45


(anonymous) @ react.development.js:1054

renderSlotElement @ copilotkit-Cd-NrDyp.mjs:88

MemoizedSlotWrapper @ copilotkit-Cd-NrDyp.mjs:96

react_stack_bottom_frame @ react-dom-client.development.js:25904

renderWithHooks @ react-dom-client.development.js:7662

updateForwardRef @ react-dom-client.development.js:9724

beginWork @ react-dom-client.development.js:12117

runWithFiberInDEV @ react-dom-client.development.js:874

performUnitOfWork @ react-dom-client.development.js:17641

workLoopSync @ react-dom-client.development.js:17469

renderRootSync @ react-dom-client.development.js:17450

performWorkOnRoot @ react-dom-client.development.js:16504

performWorkOnRootViaSchedulerTask @ react-dom-client.development.js:18957

performWorkUntilDeadline @ scheduler.development.js:45

postMessage

(anonymous) @ scheduler.development.js:225

(anonymous) @ scheduler.development.js:344

scheduleTaskForRootDuringMicrotask @ react-dom-client.development.js:18924

processRootScheduleInMicrotask @ react-dom-client.development.js:18840

(anonymous) @ react-dom-client.development.js:18991

installHook.js:1 Encountered two children with the same key, `call_6L4zojIwnOpVsBXCwFmVvCMp`. Keys should be unique so that components maintain their identity across updates. Non-unique keys may cause children to be duplicated and/or omitted — the behavior is unsupported and could change in a future version.

overrideMethod @ installHook.js:1

(anonymous) @ react-dom-client.development.js:6604

runWithFiberInDEV @ react-dom-client.development.js:871

warnOnInvalidKey @ react-dom-client.development.js:6603

reconcileChildrenArray @ react-dom-client.development.js:6672

reconcileChildFibersImpl @ react-dom-client.development.js:6993

(anonymous) @ react-dom-client.development.js:7098

reconcileChildren @ react-dom-client.development.js:9701

updateFunctionComponent @ react-dom-client.development.js:10182

beginWork @ react-dom-client.development.js:11778

runWithFiberInDEV @ react-dom-client.development.js:871

performUnitOfWork @ react-dom-client.development.js:17641

workLoopSync @ react-dom-client.development.js:17469

renderRootSync @ react-dom-client.development.js:17450

performWorkOnRoot @ react-dom-client.development.js:16504

performSyncWorkOnRoot @ react-dom-client.development.js:18972

flushSyncWorkAcrossRoots_impl @ react-dom-client.development.js:18814

flushSpawnedWork @ react-dom-client.development.js:18334

commitRoot @ react-dom-client.development.js:17955

commitRootWhenReady @ react-dom-client.development.js:16824

performWorkOnRoot @ react-dom-client.development.js:16722

performWorkOnRootViaSchedulerTask @ react-dom-client.development.js:18957

performWorkUntilDeadline @ scheduler.development.js:45

<>

(anonymous) @ react-jsx-runtime.development.js:335

(anonymous) @ copilotkit-Cd-NrDyp.mjs:4795

CopilotChatToolCallsView @ copilotkit-Cd-NrDyp.mjs:4793

react_stack_bottom_frame @ react-dom-client.development.js:25904

renderWithHooks @ react-dom-client.development.js:7662

updateFunctionComponent @ react-dom-client.development.js:10166

beginWork @ react-dom-client.development.js:11778

runWithFiberInDEV @ react-dom-client.development.js:871

performUnitOfWork @ react-dom-client.development.js:17641

workLoopSync @ react-dom-client.development.js:17469

renderRootSync @ react-dom-client.development.js:17450

performWorkOnRoot @ react-dom-client.development.js:16504

performSyncWorkOnRoot @ react-dom-client.development.js:18972

flushSyncWorkAcrossRoots_impl @ react-dom-client.development.js:18814

flushSpawnedWork @ react-dom-client.development.js:18334

commitRoot @ react-dom-client.development.js:17955

commitRootWhenReady @ react-dom-client.development.js:16824

performWorkOnRoot @ react-dom-client.development.js:16722

performWorkOnRootViaSchedulerTask @ react-dom-client.development.js:18957

performWorkUntilDeadline @ scheduler.development.js:45

(anonymous) @ react.development.js:1054

renderSlotElement @ copilotkit-Cd-NrDyp.mjs:88

MemoizedSlotWrapper @ copilotkit-Cd-NrDyp.mjs:96

react_stack_bottom_frame @ react-dom-client.development.js:25904

renderWithHooks @ react-dom-client.development.js:7662

updateForwardRef @ react-dom-client.development.js:9724

beginWork @ react-dom-client.development.js:12117

runWithFiberInDEV @ react-dom-client.development.js:874

performUnitOfWork @ react-dom-client.development.js:17641

workLoopSync @ react-dom-client.development.js:17469

renderRootSync @ react-dom-client.development.js:17450

performWorkOnRoot @ react-dom-client.development.js:16504

performSyncWorkOnRoot @ react-dom-client.development.js:18972

flushSyncWorkAcrossRoots_impl @ react-dom-client.development.js:18814

flushSpawnedWork @ react-dom-client.development.js:18334

commitRoot @ react-dom-client.development.js:17955

commitRootWhenReady @ react-dom-client.development.js:16824

performWorkOnRoot @ react-dom-client.development.js:16722

performWorkOnRootViaSchedulerTask @ react-dom-client.development.js:18957

performWorkUntilDeadline @ scheduler.development.js:45

postMessage

(anonymous) @ scheduler.development.js:225

(anonymous) @ scheduler.development.js:344

scheduleTaskForRootDuringMicrotask @ react-dom-client.development.js:18924

processRootScheduleInMicrotask @ react-dom-client.development.js:18840

(anonymous) @ react-dom-client.development.js:18991

```

### Additional Context

The exact location of the bug: [`sdks/typescript/packages/client/src/apply/default.ts` lines 302–313](https://github.com/ag-ui-protocol/ag-ui/blob/8daae85f63b1880ddc403970fd94f661c51d71c1/sdks/typescript/packages/client/src/apply/default.ts#L302-L313)

A related guard already exists in `middleware-sse-parser.ts` (CopilotKit) in the post-loop fallback for `TOOL_CALL_CHUNK` flows:

```ts
const alreadyAttached = parent.toolCalls?.some((t) => t.id === tc.id);
if (!alreadyAttached) {
parent.toolCalls.push(tc);
}
```

The same pattern just needs to be applied in `defaultApplyEvents`.

Note: `InMemoryAgentRunner.connect()` does have a de-duplication mechanism, but it only skips events with a `messageId` property (used for text messages). `TOOL_CALL_START` carries `toolCallId` instead, so it is not caught by that guard and always replays.