Home Assistant requests in a task, progress bar, Plex page, bitmap cache

- net/ha_api: the HTTP requests run in a FreeRTOS task on core 0; loop()
  only hands over copies through queues. The web UI's test button polls.
  No more 3-4 s loop() stalls once a minute; timeout raised to 5 s.
- Progress bar page element (page format 4, v3 pages are converted)
- Plex user setting (settings v6): {plex_user} in entity ids
- Plex page (examples): watchers, play/pause icon, title, progress
- Bitmaps cached in RAM: a LittleFS read took ~100 ms on every render
  and web preview; long JSON lists sent in 2 KB pieces
- Backup includes the refresh settings and the Plex user

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

src/esp32/app.cpp

@@ -91,7 +91,10 @@ static void apply()
 	controller.setEffectTime(effectTime(settings.drive));
 	status.setDrive(settings.flip_time, settings.drive, settings.refresh.dots);
 	frames.setDrive(settings.flip_time, settings.drive);
-	haApiSetSettings(settings.home_assistant);
+	char user[PLEX_USER_SIZE];
+	plexUserSlug(settings.plex_user, user, sizeof(user));
+	haApiSetSettings(settings.home_assistant, user);
+	haApiWatchRules(&page_schedule); // {plex_user} may have changed
 	applyOffPage();
 	applyPage();
 }