Instant home on reopen: snapshot of profile/grades/map/stats on the device, refreshed behind the scenes

A signed-in user with a snapshot goes straight to home; the same boot requests run in the
background and replace it. Snapshot is cleared whenever tokens are cleared and on a new login,
ignored from another build or when older than 7 days, and dropped when the fresh profile is a
different user (reboot remounts MainApp via a generation key; AnimatePresence otherwise kept the
exiting one). Notifications/characters wait for the profile answer so an expired access token
costs the same requests as before. refreshHome applies only the latest answer. Home shows a
"saved data" strip when the map could not be refreshed.

Measured locally (old vs new build, same backend, Chrome throttling, median of 3, time to map):
Fast 3G 2.46s -> 1.80s (expired token 3.63s -> 1.80s); Slow 3G 8.52s -> 6.14s (expired 12.6s ->
6.13s); API requests per open unchanged (6 valid, 11 expired). 12/12 behaviour checks passed.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

src/lib/storage.ts

@@ -31,4 +31,6 @@ export const KEYS = {
   companion: 'tadrisino.companion',
   /** {gradeId: subjectKey}؛ کتابی که کاربر در هر پایه آخر انتخاب کرده. */
   subjects: 'tadrisino.subjects',
+  /** عکسِ صفحه‌ی خانه برای بازشدنِ فوری (state/homeSnapshot.ts). */
+  homeSnapshot: 'tadrisino.homeSnapshot',
 } as const;