app-server: notify clients of remote-control status changes (#19919)

## Why

Remote-control app-server enrollments have both an internal server id
and the environment id exposed to remote-control clients. App-server
clients need one current status snapshot that says whether remote
control is usable and which environment id, if any, is exposed.

A temporary websocket disconnect is not itself an identity change.
Account changes, stale enrollment invalidation, successful
re-enrollment, and missing ChatGPT auth are meaningful status changes.
Disabled remote control remains `disabled` regardless of auth or SQLite
state. SQLite startup failure disablement and enrollment persistence
failures are handled in #20068; this PR reports the resulting effective
status to clients.

## What changed

- Adds v2 `remoteControl/status/changed` carrying `state` and
`environmentId`.
- Adds `RemoteControlConnectionState` values: `disabled`, `connecting`,
`connected`, and `errored`.
- Exposes remote-control status updates through `RemoteControlHandle`
using a Tokio watch channel.
- Always sends the current remote-control status snapshot to newly
initialized app-server clients.
- Broadcasts status changes to initialized app-server clients when state
or environment id changes.
- Treats missing ChatGPT auth as an `errored` status while leaving it
retryable because auth can change at runtime.
- Clears `environmentId` when enrollment is cleared for account changes,
auth loss, stale backend invalidation, or disabled remote control.
- Updates app-server protocol schema fixtures, generated TypeScript,
app-server README, remote-control tests, and TUI exhaustive notification
matches.

## Stack

- Builds on #20068.

## Verification

- `just write-app-server-schema`
- `cargo test -p codex-app-server-protocol`
- `cargo test -p codex-app-server transport::remote_control --lib`
- `cargo check -p codex-tui`
- `just fix -p codex-app-server-protocol`
- `just fix -p codex-app-server`
- `just fix -p codex-tui`

codex-rs/app-server-protocol/schema/json/ServerNotification.json

@@ -2603,6 +2603,33 @@
       ],
       "type": "object"
     },
+    "RemoteControlConnectionStatus": {
+      "enum": [
+        "disabled",
+        "connecting",
+        "connected",
+        "errored"
+      ],
+      "type": "string"
+    },
+    "RemoteControlStatusChangedNotification": {
+      "description": "Current remote-control connection status and environment id exposed to clients.",
+      "properties": {
+        "environmentId": {
+          "type": [
+            "string",
+            "null"
+          ]
+        },
+        "status": {
+          "$ref": "#/definitions/RemoteControlConnectionStatus"
+        }
+      },
+      "required": [
+        "status"
+      ],
+      "type": "object"
+    },
     "RequestId": {
       "anyOf": [
         {
@@ -5342,6 +5369,26 @@
       "title": "App/list/updatedNotification",
       "type": "object"
     },
+    {
+      "properties": {
+        "method": {
+          "enum": [
+            "remoteControl/status/changed"
+          ],
+          "title": "RemoteControl/status/changedNotificationMethod",
+          "type": "string"
+        },
+        "params": {
+          "$ref": "#/definitions/RemoteControlStatusChangedNotification"
+        }
+      },
+      "required": [
+        "method",
+        "params"
+      ],
+      "title": "RemoteControl/status/changedNotification",
+      "type": "object"
+    },
     {
       "properties": {
         "method": {