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/src/message_processor.rs

@@ -40,6 +40,7 @@ use crate::request_processors::ThreadGoalRequestProcessor;
 use crate::request_processors::ThreadRequestProcessor;
 use crate::request_processors::TurnRequestProcessor;
 use crate::request_processors::WindowsSandboxRequestProcessor;
+use crate::request_processors::read_server_diagnostics;
 use crate::request_serialization::QueuedInitializedRequest;
 use crate::request_serialization::RequestSerializationQueueKey;
 use crate::request_serialization::RequestSerializationQueues;
@@ -900,6 +901,7 @@ impl MessageProcessor {
             ClientRequest::Initialize { .. } => {
                 panic!("Initialize should be handled before initialized request dispatch");
             }
+            ClientRequest::ServerDiagnostics { .. } => Ok(Some(read_server_diagnostics().into())),
             ClientRequest::ConfigRead { params, .. } => self
                 .config_processor
                 .read(params)