MCP App iframe stops responding on mobile when UI content changes (e.g., filtering a list)

### What happened?

Hi team, I created an MCP App has filter tabs that update a React state to show/hide list items — pure client-side, no server calls. On desktop it works fine. On mobile (Claude iOS app and Chrome mobile emulation on Claude web), the iframe freezes after 1-2 clicks.

- Same widget code tested in a standalone sandboxed iframe on mobile emulation works perfectly — the freeze only happens inside Claude's host page.

### What did you expect to happen?

Client-side interactions inside an MCP App iframe (filter tabs, toggles, etc.) should remain responsive on mobile, same as desktop.

### Steps to reproduce

No mobile device needed:

1. Open a Claude conversation with an MCP App that has interactive elements (buttons/tabs that change displayed content on click)
2. Open Chrome DevTools → toggle device toolbar → select any mobile device (e.g., iPhone 14 Pro Max)
3. Click the interactive elements a few times
4. After 1-2 clicks, the iframe stops responding
5. Turn off device emulation → same page works immediately

### Area

Other

### MCP Server (if applicable)

Custom server using `@modelcontextprotocol/sdk`. Server-side is not relevant — the widget works in non-Claude iframes.

### Error messages or logs

```shell
No error messages in console when the freeze occurs
```

### Additional context

- SDK: `@modelcontextprotocol/ext-apps` v1.1.2, React 18
- Tested with `autoResize: false` — same result
- Performance traces show click events reach the iframe (INP ~15-20ms) but the render pipeline stops running on mobile
- `anthropic.com` main thread time: ~20ms on desktop vs ~200ms on mobile emulation

#### Questions:
1. Is this a known issue or by design?
2. Is there a recommended workaround for MCP Apps that need client-side interactivity on mobile?
3. Should interactive MCP Apps (tabs, toggles, filters) be expected to work on mobile, or is this not yet supported?