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/commands/connection.rs

@@ -1017,7 +1017,7 @@ pub async fn connection_final_proxy_port(
 
 #[tauri::command]
 pub async fn disconnect_db(state: State<'_, Arc<AppState>>, connection_id: String) -> Result<(), String> {
-    state.remove_connection_pools_detached(&connection_id).await;
+    state.remove_connection_pools(&connection_id).await;
     drop_mq_adapters_for_connection_ids(state.inner(), std::slice::from_ref(&connection_id)).await;
     state.reset_connection_transport(&connection_id).await;
     if connection_id.starts_with("__visible_draft_") {
@@ -1043,6 +1043,11 @@ pub async fn refresh_connections(state: State<'_, Arc<AppState>>) -> Result<(),
     Ok(())
 }
 
+#[tauri::command]
+pub async fn check_connection_health(state: State<'_, Arc<AppState>>, connection_id: String) -> Result<(), String> {
+    state.check_connection_health(&connection_id).await
+}
+
 /// Check whether a connection has read-only protection enabled.
 /// Returns an error if the connection is read-only, preventing write operations.
 pub async fn ensure_connection_writable(