Custom OAuth MCP connector tools not surfaced in mobile chat (works on desktop/web)

### What happened?

Custom remote MCP connector with OAuth completes authentication successfully, and server logs confirm the discovery handshake and tools/list respond with HTTP 200. However, on the iOS app the connector never shows as usable — no tool badge appears, and the UI stays on "Connect." In chat, the assistant reports the connector isn't available as a tool.

This appears related to #472, which describes the same session-restart / discovery-without-invocation pattern on mobile.

Repro steps:
1. Add a custom OAuth MCP connector (also tested with a freshly created connector — same result).
2. Complete OAuth on iOS. Server-side logs confirm successful handshake + tools/list 200.
3. iOS app never shows the tool badge; chat says the connector isn't available as a tool.

Controls:
- A different, smaller connector on the same device/account works normally (tool badge appears, tools invocable in chat).
- The same custom connector works correctly on Claude desktop/web, full tool catalog invocable.
- The connector is visible for artifacts on mobile, but not invocable in conversation — so it's not a total auth failure, just a tool-surfacing issue specific to chat.

Additional test: reduced the connector's tool catalog to a small handful of tools to rule out payload size as a factor. Same failure — still no badge on mobile. Points to a client-side issue in how discovery is wired to invocation for custom (non-directory) connectors, specific to the mobile chat surface.

Already reported via official in-app support as well.

### What did you expect to happen?

Expected the custom connector to behave the same way it does on desktop/web: once OAuth completes and tools/list returns successfully, the tools should be available and invocable in mobile chat, with a visible tool badge — consistent with how other (smaller/directory) connectors already work on the same device and account.

### Steps to reproduce

1. Add a custom OAuth MCP connector on Claude mobile (iOS). Also tested with a freshly created connector name — same result.
2. Complete OAuth on the iPhone. Server-side logs confirm the discovery handshake and tools/list respond with HTTP 200.
3. Return to chat and try to use a tool from the connector.
4. See: no tool badge ever appears on the connector; the app UI stays on "Connect." In chat, the assistant reports the connector isn't available as a tool.

Controls tried:
- A different, smaller connector on the same device/account works normally (badge appears, tools invocable in chat).
- The same custom connector works correctly on Claude desktop/web, with its full tool catalog invocable.
- The connector does show up when building an artifact on mobile, just not as an invocable tool in regular chat.
- Reduced the connector's tool catalog to a small handful of tools to rule out payload size — same failure, still no badge on mobile.

### Area

MCP Connector (adding/managing servers)

### MCP Server (if applicable)

_No response_

### Error messages or logs

```shell

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### Additional context

_No response_