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>

docs/pages.md

@@ -20,3 +20,4 @@ the others are the example pages in [examples/home-pages.json](../examples/home-
 | **Datum**: weekday and date | ![Datum](../Pictures/pages/datum.png) |
 | **Aftellen**: countdown to Christmas | ![Aftellen](../Pictures/pages/aftellen.png) |
 | **Stopwatch** | ![Stopwatch](../Pictures/pages/stopwatch.png) |
+| **Plex**: how many watch, play/pause, title (scrolls) and progress of the Plex user ([Tautulli](home-assistant.md#plex-and-tautulli)) | ![Plex](../Pictures/pages/plex.png) |