## Why
App-server clients need to advertise structured MCP extension settings, including supported MCP App UI MIME types, rather than only opting into OpenAI form elicitation with a boolean.
## What changed
- Add an `extensions` map to initialize capabilities and preserve `mcpServerOpenaiFormElicitation` as a legacy alias for `openai/form`.
- Capture the declared extension profile when a thread is started, resumed, or forked, propagate it to subagents, and advertise it to downstream MCP servers during initialization.
- Keep the profile stable for the lifetime of the loaded session instead of changing it on later turns or direct tool calls.
## Testing
- Cover extension conversion, downstream MCP initialization, session isolation, legacy form support, and subagent inheritance.
GitOrigin-RevId: fbcedbb74ce788e574b0f884a4c45c4cedb9de54
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