[Feat] Give Fast mode deployment MCP access - #1604

- Exclude user-scoped curated integrations from Fast config resolution;
  their API proxies reject control-plane auth tokens, so they failed
  discovery on every turn.
- Re-mint the broker auth token at integration call time for
  deployment-proxy endpoints instead of reusing the short-lived
  list-time token, which expired mid-turn on long turns.
- Pass a consistent apiBaseUrl through parent-event Fast turns so the
  broker's origin check keeps injecting proxy auth on split-origin
  deployments.
- Add an onError handler and safe JSON parsing to the in-process
  custom-automations app so router failures surface as structured tool
  errors, and keep the numeric HTTP status from being clobbered by a
  response body's own status field.
- Return early from integration listing when no MCP servers or GitHub
  installation exist, restoring the pre-existing quiet no-op path.
- Warn when a Fast surface provides no MCP config resolver instead of
  silently serving zero deployment servers.
- Prune expired per-user entries from the integration tool cache.
- Silence the per-connection config-resolution info logging on the
  per-turn Fast path.
- Document Fast-mode automation management and MCP server access.

- Extract buildManageCustomAutomationsRequest into @roomote/types so the
  worker MCP server and the API-hosted tool map actions onto the
  custom-automations REST routes from one source instead of two
  hand-kept switches (which had already drifted on body filtering).
- Extract a shared in-process API invocation helper for MCP tool
  handlers; the member tools and custom-automations tool now share the
  auth-impersonation app, onError handler, safe JSON parsing, and
  status-preserving error shape (member tools previously lacked the
  error handler and let response bodies clobber the HTTP status).
- Add ROOMOTE_MCP_ID and MCP proxy path-prefix constants to
  @roomote/types and use them at every producer and consumer, so the
  security-relevant 'roomote' gating and deployment-proxy detection
  cannot silently diverge from the URLs being built.
- Collapse createRoomoteMcpServer's two identical auth params into one
  plus a boolean.
- Route Discord and parent-event Fast surfaces through the canonical
  resolveApiBaseUrl fallback chain instead of inline env fallbacks.