## Why
An empty tool map does not distinguish a successfully returned empty catalog from a server whose startup or tool discovery failed.
## What changed
- Add nullable `toolsError` to each `mcpServerStatus/list` entry when no catalog is available because startup or tool discovery failed.
- Keep `toolsError` null for returned catalogs, including cached and empty catalogs, and continue returning healthy servers when another server fails.
- Update the protocol schemas and generated TypeScript type.
## Testing
- Extend the app-server status integration test with a broken MCP server and verify its error without losing the healthy server's inventory.
GitOrigin-RevId: 30b4ca4d9a45cec6998f5f626d3fddbee90a525d