fix: resolve MySQL connection state desync after disconnect/reconnect

- Use synchronous pool removal in desktop disconnect_db to prevent
  race condition when user quickly disconnects and reconnects
- Rename recordMetadataLoadError to recordConnectionLostError and
  export it for cross-store reuse
- Sync query execution errors back to connection state via
  recordConnectionLostError in queryStore catch blocks
- Add backend check_connection_health method (dbx-core) with Tauri
  command and web route for proactive pool verification
- Add frontend checkConnectionHealth API (tauri.ts/http.ts/api.ts)
- Enhance ensureConnected to verify backend pool health before
  assuming connection is valid, auto-reconnect if stale

src-tauri/src/lib.rs

@@ -423,6 +423,7 @@ pub fn run() {
             commands::connection::disconnect_db,
             commands::connection::close_database_connection,
             commands::connection::refresh_connections,
+            commands::connection::check_connection_health,
             commands::connection::save_connections,
             commands::connection::load_connections,
             commands::connection::save_sidebar_layout,