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/logic/settings.h

@@ -83,6 +83,8 @@ struct Settings
 	char off_page[PAGE_NAME_SIZE] = OFF_PAGE_BLANK;
 	DriveSettings drive;
 	RefreshSettings refresh;
+	// Plex user name for {plex_user} in entity ids (Tautulli's sensors of that user)
+	char plex_user[PLEX_USER_SIZE] = "";
 	// New fields go here, at the end (see system/settings_store.cpp)
 };