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/request_processors/diagnostics.rs

@@ -0,0 +1,23 @@
+use codex_app_server_protocol::ServerDiagnosticsGauge;
+use codex_app_server_protocol::ServerDiagnosticsProcess;
+use codex_app_server_protocol::ServerDiagnosticsResponse;
+
+pub(crate) fn read_server_diagnostics() -> ServerDiagnosticsResponse {
+    let diagnostics = codex_diagnostics::snapshot();
+
+    ServerDiagnosticsResponse {
+        process: ServerDiagnosticsProcess {
+            id: diagnostics.process.id,
+            resident_memory_bytes: diagnostics.process.resident_memory_bytes,
+            physical_footprint_bytes: diagnostics.process.physical_footprint_bytes,
+        },
+        gauges: diagnostics
+            .gauges
+            .into_iter()
+            .map(|gauge| ServerDiagnosticsGauge {
+                name: gauge.name.to_string(),
+                value: gauge.value,
+            })
+            .collect(),
+    }
+}