[codex] misc sync and startup fixes

[kalzEOS]

What changed

• Added a periodic background sync scheduler and worker.
• Added settings for refresh-on-startup and configurable sync intervals.
• Tightened the auth startup flow so the login screen does not flash before saved config loads.
• Kept the existing fast-start/full-sync flow and cache checkpoints aligned with the new background sync behavior.

Why

• The app needs automatic library refreshes without manual throttling.
• Startup auth state needed to wait for persisted config before rendering the login screen.
• The new sync controls needed to persist and restore cleanly after process restarts.

Validation

• ./gradlew :app:compileDebugKotlin

[chatgpt-codex-connector]

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[chatgpt-codex-connector]

Prevent worker/app sync overlap

When a scheduled sync starts while the app is not already syncing, this one-time check passes and the worker never reserves the cache for its own writes; if the user opens the app or triggers a manual/progressive sync before the worker finishes, ProgressiveSyncCoordinator can also enter syncBackgroundFull and both jobs write the same section index/checkpoint temp files. Use a shared guard or mutex that the worker holds around syncBackgroundFull and that app sync also honors, rather than only doing this preflight check.

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