ui/update-model-context is accepted but never reaches the model (Claude Desktop 1.26832.0)

### What happened?

An MCP App calls `updateModelContext()` after the user clicks in its panel. The host
advertises the capability, accepts the request, and returns a successful (empty)
result — but the model has no access to the content, on that turn or any later one.
When asked about it directly, the model reports that no such channel exists.

This is the same symptom as #102, which was closed on the grounds that the host
"offloads the model context and lets the model fetch it with a tool". That fetch path
is not reachable here.

### What did you expect to happen?

**Expected**

Per the SDK docs, the host defers the update and includes the last one with the next
user message. Per #102's closing comment, the model can instead fetch it with a tool.
Either would let the model answer from what the panel currently shows.

**Actual**
The content is acknowledged and then unavailable to the model by any route. The model
answers from the last tool result it issued itself, which is stale as soon as the user
clicks once.

### Steps to reproduce

1. Serve an MCP App that calls `updateModelContext` with a text block after a
user-driven `callServerTool`.
2. In Claude Desktop, have the model open the app, then click within the panel so its
state changes.
3. Ask what the panel is showing.

### Area

Tool Discovery / Invocation

### MCP Server (if applicable)

_No response_

### Error messages or logs

```shell

```

### Additional context

- The same app, in a host that folds the update into the prompt, answers correctly —
so the app-side call is well-formed.
- #102 reported this for Claude web and was closed as completed on 2026-04-24.