Use installed callable apps for TUI mentions (#39051)

## Why

The app directory is a discovery catalog and can include apps that are not
callable in the active thread. Using it for `$` suggestions can therefore
offer mentions that cannot be used.

## What changed

- Load mention candidates from `app/installed`, enrich callable apps through
  bounded `app/read` batches, and retain compatibility with app servers that
  do not support `app/installed`.
- Keep the mention catalog separate from the `/apps` directory cache and scope
  results to the current thread, workspace, and account.
- Refresh mentions after app notifications, enablement changes, configuration
  updates, and apps MCP readiness, while immediately removing disabled apps.

## Testing

Add coverage for batching and fallback behavior, stale scoped results,
notification refreshes, enablement changes, MCP startup races, and filtering
non-callable apps from mentions.

GitOrigin-RevId: 4d9e20794aed30cc97120170792fb555b86fe1e7

codex-rs/tui/src/app_event.rs

@@ -510,6 +510,14 @@ pub(crate) enum AppEvent {
         is_final: bool,
     },
 
+    /// Thread-scoped installed applications that may actually be mentioned.
+    InstalledConnectorMentionsLoaded {
+        thread_id: Option<ThreadId>,
+        cwd: PathBuf,
+        generation: ConnectorScopeGeneration,
+        result: Result<ConnectorsSnapshot, String>,
+    },
+
     /// Result of computing a `/diff` command.
     DiffResult(PathBuf, String),
 
@@ -577,6 +585,12 @@ pub(crate) enum AppEvent {
         generation: ConnectorScopeGeneration,
     },
 
+    /// Refresh callable installed applications without loading the app directory.
+    FetchInstalledConnectorMentions {
+        force_refresh: bool,
+        generation: ConnectorScopeGeneration,
+    },
+
     /// Fetch plugin marketplace state for the provided working directory.
     FetchPluginsList {
         cwd: PathBuf,