Expose app-server diagnostics through the experimental API (#37470)

## What changed

- Add the experimental `server/diagnostics` request, returning the app-server process ID, resident memory, platform-dependent physical footprint, and registered diagnostic gauges.
- Export the new protocol types in the generated JSON and TypeScript schemas and document the request.

## Testing

- Verify the response includes process measurements and the registered live-thread gauge.
- Verify the request is rejected unless `capabilities.experimentalApi` is enabled.

GitOrigin-RevId: 099d60a9c421a74ff1a72fe524e0dfeb89cf1057

codex-rs/app-server-protocol/src/protocol/common.rs

@@ -478,6 +478,14 @@ client_request_definitions! {
         response: v1::InitializeResponse,
     },
 
+    #[experimental("server/diagnostics")]
+    /// Read content-free, process-local diagnostics.
+    ServerDiagnostics => "server/diagnostics" {
+        params: v2::ServerDiagnosticsParams,
+        serialization: None,
+        response: v2::ServerDiagnosticsResponse,
+    },
+
     /// NEW APIs
     // Thread lifecycle
     // Uses `inspect_params` because only some fields are experimental.