Wire up the phone/watch sync bridge (issue #276)

[mapitman]

Summary

Step 4 of #276 (see #278-280 for steps 1-3). The phone now pushes its Next Up queue and playback position to a paired watch, and applies position reports back from it, both directions durable to either device being briefly unreachable.

• QueueSyncPublisher (:app) debounces QueueRepository.observeQueue() and pushes snapshots via WearSyncClient; started from MainActivity.onCreate (not Application.onCreate, which also runs under every Robolectric-hosted unit test — same reasoning as the existing feedRefreshScheduler wiring already there).
• PlaybackService's existing 5s position-save loop now also pushes to WearSyncClient alongside its local FeedRepository write.
• PositionSyncApplier (:core) applies an incoming position update last-write-wins by timestamp; shared by both apps' manifest-registered WearableListenerService (WearSyncListenerService on :wear, PhoneSyncListenerService on :app), which wake the process even when it isn't already running.
• WearQueueSyncApplier (:wear) applies an incoming queue snapshot into the watch's own local Room database (upserting the referenced Feed rows first, for the feed_items FK).
• QueueRepository's download trigger is a no-op on the watch in phase 1 (NoOpQueueDownloadTrigger) — streaming only, downloads are phase 2 (Send downloaded episodes to Wear OS for offline playback (phase 2) #277).

Moved PlayServicesWearSyncClient (added in #280 under :wear) into :core along with its Hilt bindings, since :app now needs the same DataClient-backed WearSyncClient — Hilt's per-app module discovery means defining it once in :core wires it into both apps' components for free, avoiding a duplicate copy in each.

Hit and fixed a real bug along the way: an early version started the queue publisher from Application.onCreate(), which caused every Robolectric-hosted :app unit test to spin up a background coroutine hitting a real database file and real Play Services. Moved the start call to MainActivity.onCreate() instead, matching the codebase's existing pattern for exactly this kind of startup work.

Test plan

• ./gradlew assembleDebug testDebugUnitTest lintDebug passes across :app/:core/:wear
• New unit tests: QueueSyncPublisherTest (debounce/coalescing, failure resilience — against a virtual-time-controlled Flow rather than Room's real-dispatcher-backed one, which proved unreliable to assert exact timing against), PositionSyncApplierTest (last-write-wins), WearQueueSyncApplierTest (Room upsert/replace behavior)
• Installed and launched both debug builds (phone emulator + mycasts_wear_test Wear OS emulator) — confirmed no crash on either
• Not verified: a live phone↔watch sync round trip. That needs the two emulators (or a real watch) actually paired, which is separate setup from anything this PR touches — noted as a manual follow-up.