Add turn trigger metadata (#40665)

## What changed

- Add an optional `turnTrigger` field to app-server `turn/start` requests and
  expose it in the generated protocol schemas.
- Propagate non-empty trigger values to Responses request metadata as the
  reserved `turn_trigger` field, while preserving the original value when a
  request steers an active turn.
- Classify turns started by queue dispatch, goal continuation, retry recovery,
  and realtime handoff.

## Testing

- Cover HTTP and WebSocket metadata forwarding, steering behavior, reserved
  metadata handling, and the built-in trigger classifications.

GitOrigin-RevId: c12fe2c522286db21b76081ae6154fbf6bfb3639

codex-rs/app-server-protocol/schema/json/v2/TurnStartParams.json

@@ -675,6 +675,13 @@
     },
     "threadId": {
       "type": "string"
+    },
+    "turnTrigger": {
+      "description": "Optional source classification for the caller that starts this turn. Ignored when this request steers an already-active turn.",
+      "type": [
+        "string",
+        "null"
+      ]
     }
   },
   "required": [