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/main.cpp

@@ -62,6 +62,7 @@ void setup()
 	status.show("Getting", "the time...", true);
 
 	configTzTime(TIMEZONE, NTP_SERVER);
+	haApiBegin(); // Home Assistant values are read in a task of their own
 	homeAssistantBegin(controller, appSettings().home_assistant);
 	webUiBegin();
 
@@ -80,7 +81,7 @@ void loop()
 	homeAssistantLoop();
 	webUiLoop();
 	appLoop();
-	// Home Assistant values of the shown page (can block about 3 s once a minute)
+	// Home Assistant values of the shown page (read by a task, never blocks)
 	if (haApiLoop(wifiConnected()))
 		controller.pageChanged();