Fix double apply, cache loss, and hidden failures on rotation start

[codenameakshay]

Three rotation-start bugs, all reproduced on an API 36 emulator:

	Before	After
Start	Applied twice. Start applied the first image, and WorkManager then ran the new periodic request at once, which skipped ahead	One apply. The first scheduled run waits one interval
Rejected start (every source fails)	Deleted the running rotation's cache. Status still said "running", but every rotation failed	Cache untouched, and Rotate now still works
One of two sources fails	"index 0 of 1, 1 cached", so the failure was hidden	"index 0 of 2, 1 cached"

 startRotation
-  delete the cache dir, then cache sources into it
+  cache into <cache>.staging; swap it in only if at least one source loaded
   save config (+ requestedSourceCount)
   apply the first wallpaper
 schedulePeriodic / scheduleCharging
+  setInitialDelay(interval)

Verification

API 36 emulator, checked with dumpsys wallpaper ids and logcat:

• Start: the wallpaper id goes 27 → 28, and no worker runs in the next 20 s. Before, it went 22 → 24, with the worker running 0.4 s after start.
• Rejected start: wallpaper_0.jpg and wallpaper_1.jpg survive, and Rotate now succeeds.
• Partial failure: the status shows 2 requested and 1 cached.

Tests: JVM tests cover the staging swap (a reject keeps the cache, an accept replaces it) and the WorkManager initial delay. Plugin unit tests: 63 pass.

Local CI (format, analyze, tests, pigeon check, Gradle test/lint/assemble, iOS simulator build): pass.

🤖 Generated with Claude Code