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/src/protocol/common.rs

@@ -1258,6 +1258,7 @@ server_notification_definitions! {
     AccountUpdated => "account/updated" (v2::AccountUpdatedNotification),
     AccountRateLimitsUpdated => "account/rateLimits/updated" (v2::AccountRateLimitsUpdatedNotification),
     AppListUpdated => "app/list/updated" (v2::AppListUpdatedNotification),
+    RemoteControlStatusChanged => "remoteControl/status/changed" (v2::RemoteControlStatusChangedNotification),
     ExternalAgentConfigImportCompleted => "externalAgentConfig/import/completed" (v2::ExternalAgentConfigImportCompletedNotification),
     FsChanged => "fs/changed" (v2::FsChangedNotification),
     ReasoningSummaryTextDelta => "item/reasoning/summaryTextDelta" (v2::ReasoningSummaryTextDeltaNotification),

codex-rs/app-server-protocol/src/protocol/v2.rs

@@ -2878,6 +2878,25 @@ pub struct DeviceKeyPublicResponse {
     pub protection_class: DeviceKeyProtectionClass,
 }
 
+/// Current remote-control connection status and environment id exposed to clients.
+#[derive(Serialize, Deserialize, Debug, Clone, PartialEq, Eq, JsonSchema, TS)]
+#[serde(rename_all = "camelCase")]
+#[ts(export_to = "v2/")]
+pub struct RemoteControlStatusChangedNotification {
+    pub status: RemoteControlConnectionStatus,
+    pub environment_id: Option<String>,
+}
+
+#[derive(Serialize, Deserialize, Debug, Clone, Copy, PartialEq, Eq, JsonSchema, TS)]
+#[serde(rename_all = "camelCase")]
+#[ts(rename_all = "camelCase", export_to = "v2/")]
+pub enum RemoteControlConnectionStatus {
+    Disabled,
+    Connecting,
+    Connected,
+    Errored,
+}
+
 /// Audience for a remote-control client connection device-key proof.
 #[derive(Serialize, Deserialize, Debug, Clone, Copy, PartialEq, Eq, JsonSchema, TS)]
 #[serde(rename_all = "snake_case")]