[DAV-022] Native tasks UX

[veryCrunchy]

Roadmap

• Task ID: DAV-022
• Priority: P1
• Parent epic: [EPIC] DAV device sync and native groupware #12
• Related sync foundation: [DAV-001] Android account model #20, [DAV-002] Principal, home-set, and collection discovery store #21, [DAV-003] Collection selection UI #22, [DAV-006] Task provider integrations #25, [DAV-007] Incremental sync-token engine #26, [DAV-009] Conflict-safe DAV upload/delete #28, [DAV-019] Sync status and error UI #38

Acceptance criteria

• Present task calendars and native All, Current, Today, Week, Important, Completed, Calendar, and Category collections.
• Support search, parent-child task hierarchy, subtasks, due states, priority, recurrence, categories, and read-only calendars.
• Provide adaptive compact navigation and a persistent desktop task inspector.
• Show loading, empty, cached-error, retry, and no-writable-calendar states.
• Plan create, update, complete, reopen, and delete operations with verified CalDAV identity, ETag, conflict, and destructive-action handling.
• Preserve task data fidelity and never silently overwrite a conflicting server revision.
• Cover compact phone, large phone, and desktop behavior with deterministic tests and synthetic visual QA.
• Verify read behavior against a real authenticated account before enabling carefully bounded write tests.