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/core/src/session/session.rs

@@ -17,6 +17,7 @@ use codex_protocol::SessionId;
 use codex_protocol::capabilities::SelectedCapabilityRoot;
 use codex_protocol::config_types::SERVICE_TIER_DEFAULT_REQUEST_VALUE;
 use codex_protocol::config_types::ServiceTier;
+use codex_protocol::mcp::ClientMcpExtensions;
 use codex_protocol::permissions::FileSystemPath;
 use codex_protocol::permissions::FileSystemSpecialPath;
 use codex_protocol::protocol::MultiAgentVersion;
@@ -515,7 +516,7 @@ impl Session {
         code_mode_session_provider: Arc<dyn codex_code_mode::CodeModeSessionProvider>,
         extensions: Arc<codex_extension_api::ExtensionRegistry<crate::config::Config>>,
         mut thread_extension_init: ExtensionDataInit,
-        supports_openai_form_elicitation: bool,
+        client_mcp_extensions: ClientMcpExtensions,
         agent_control: AgentControl,
         environment_manager: Arc<EnvironmentManager>,
         inherited_environments: Option<TurnEnvironmentSnapshot>,
@@ -1126,9 +1127,7 @@ impl Session {
                 thread_extension_data,
                 selected_capability_roots,
                 mcp_thread_init,
-                supports_openai_form_elicitation: std::sync::atomic::AtomicBool::new(
-                    supports_openai_form_elicitation,
-                ),
+                client_mcp_extensions,
                 agent_control,
                 network_proxy: arc_swap::ArcSwapOption::from(network_proxy.map(Arc::new)),
                 network_proxy_audit_metadata,