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.cpp

@@ -41,7 +41,7 @@ const char *validateSettings(const Settings &s)
 	const HomeAssistantSettings &ha = s.home_assistant;
 	if (!terminated(ha.host, sizeof(ha.host)) || !terminated(ha.user, sizeof(ha.user)) ||
 		!terminated(ha.password, sizeof(ha.password)) || !terminated(ha.api_url, sizeof(ha.api_url)) ||
-		!terminated(ha.token, sizeof(ha.token)))
+		!terminated(ha.token, sizeof(ha.token)) || !terminated(s.plex_user, sizeof(s.plex_user)))
 		return "Home Assistant text too long";
 	if (ha.port == 0)
 		return "Invalid MQTT port";