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>

CLAUDE.md

@@ -172,8 +172,18 @@ See README.md for the overview.
   after adding features; the web page could be served gzipped if it gets tight.
 - Fonts use the "FDF1" format of `logic/font.h`; the web page writes the same format.
   `logic/builtin_fonts.cpp` is generated: change `tools/make_builtin_fonts.py` and rerun it.
-- Home Assistant values come from HA's REST API (`net/ha_api`), one blocking request per
-  `loop()` with `HA_HTTP_TIMEOUT`. Keep it that way (watchdog, OTA).
+- Home Assistant values come from HA's REST API (`net/ha_api`). The HTTP requests run in
+  their own FreeRTOS task (core 0, `haApiBegin()`), one at a time; everything else
+  (entries, watching, values) stays in `loop()`. The task gets copies of what it needs and
+  answers through a queue of plain structs: never share Strings or other state with it,
+  and never wait for it in `loop()`. The web UI's test button polls (`{"pending":true}`).
+  The web server stays in `loop()` on purpose (its handlers touch everything).
+- Entity ids may contain `{plex_user}` (`expandEntity()` in `logic/page`), filled in by
+  `net/ha_api` with `settings.plex_user` in entity id form (`plexUserSlug()`).
+- Bitmaps are cached in RAM (`display/bitmap_store`, also missing names): a LittleFS read
+  takes about 100 ms, and pages are drawn for every frame and every web preview. Writes
+  must go through `saveBitmap()`/`deleteBitmap()`, which clear the cache. Long JSON lists
+  are sent in pieces of about 2 KB (`sendPiece()` in `web_ui.cpp`).
 - Check the page's JavaScript after changes: extract the `<script>` part and run
   `node --check` on it (node is installed).