Self-update for app and installer. Integrates cleanly with the
worker-log-footer feature that landed on main in parallel — the
shell VM now carries both worker-log state and update-check state,
and MainWindow hosts both the update banner and the footer log line.
Conflict resolved in IslandsShellViewModel.cs: kept nullable property
types from main's test-only parameterless constructor work, and added
the UpdateCheck property exposing the injected service.
Parses Claude CLI stream-json output into human-readable text.
Handles text deltas, tool use, results, API retries, and trims large files.
All 13 tests pass.
Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
