fix(mount): guard operations when provider mounts are not ready

[samtruman]

Summary

Prevent mount-dependent operations from treating an unavailable FUSE/provider
mount as a valid empty filesystem.

What changed

• add a shared, source-scoped readiness probe using the native mount table and
  a bounded filesystem response check;
• evaluate configured provider and WebDAV sources independently;
• let available sources continue while unavailable sources are skipped;
• suspend Organizer pruning whenever a configured source is not observable;
• return a not-ready response for aggregate mounted-filesystem browsing;
• preserve valid empty mounted filesystems as distinct from unavailable ones.

Safety

NOT READY is never interpreted as EMPTY. No pruning or destructive
filesystem mutation is derived from an unobservable source.

Tests

Added synthetic readiness and Organizer safety coverage for mounted,
unavailable, empty, recovery, and multi-source cases.

Validation: 91 tests passed, typecheck passed, backend build passed, and
git diff --check passed.