Negotiate MCP extensions per app-server session (#36910)

## 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

codex-rs/app-server-protocol/schema/json/codex_app_server_protocol.v2.schemas.json

@@ -8326,8 +8326,16 @@
           "description": "Opt into receiving experimental API methods and fields.",
           "type": "boolean"
         },
+        "extensions": {
+          "additionalProperties": true,
+          "description": "MCP extension settings declared by the app-server client.",
+          "type": [
+            "object",
+            "null"
+          ]
+        },
         "mcpServerOpenaiFormElicitation": {
-          "description": "Allow downstream MCP servers to request OpenAI extended form elicitations.",
+          "description": "Legacy opt-in for the `openai/form` MCP extension.\n\nNew clients should declare `openai/form` in [`Self::extensions`].",
           "type": "boolean"
         },
         "optOutNotificationMethods": {