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/analytics/src/analytics_client_tests.rs

@@ -822,6 +822,7 @@ fn sample_initialize_fact(connection_id: u64) -> AnalyticsFact {
                 request_attestation: false,
                 opt_out_notification_methods: None,
                 mcp_server_openai_form_elicitation: false,
+                extensions: None,
             }),
         },
         product_client_id: DEFAULT_ORIGINATOR.to_string(),
@@ -1883,6 +1884,7 @@ async fn initialize_caches_client_and_thread_lifecycle_publishes_once_initialize
                         request_attestation: false,
                         opt_out_notification_methods: None,
                         mcp_server_openai_form_elicitation: false,
+                        extensions: None,
                     }),
                 },
                 product_client_id: DEFAULT_ORIGINATOR.to_string(),
@@ -2188,6 +2190,7 @@ async fn compaction_event_ingests_custom_fact() {
                         request_attestation: false,
                         opt_out_notification_methods: None,
                         mcp_server_openai_form_elicitation: false,
+                        extensions: None,
                     }),
                 },
                 product_client_id: DEFAULT_ORIGINATOR.to_string(),
@@ -2319,6 +2322,7 @@ async fn guardian_review_event_ingests_custom_fact_with_optional_target_item() {
                         request_attestation: false,
                         opt_out_notification_methods: None,
                         mcp_server_openai_form_elicitation: false,
+                        extensions: None,
                     }),
                 },
                 product_client_id: DEFAULT_ORIGINATOR.to_string(),