Make daily traffic scale to dozens of screens: incremental sync, ping keepalive, one action per message (0.2.39)

App 0.2.39 / firmware 0.2.33, items 1, 2, 4, 5 and 6 of the 30-screen scaling check.

- Only the tiles (and top bar) of changed entities are rebuilt; the screen list is
  cached until the registry or a screen diagnostic changes; the SSE stream follows.
- Sensor history comes from one recorder/statistics_during_period call per window in
  a background task, with the REST history as fallback per sensor without statistics.
- Firmware 0.2.33 answers a keepalive ping with its layout revision; a mismatch or a
  restart asks for the layout again, everything is repeated hourly as a safety net.
- The screen_message API action takes one whole message; the text inbox chunks stay
  as fallback for older firmware. A repeated unchanged layout keeps the inbox state.
- Quiet diagnostics: Opgestart (uptime as timestamp) replaces Uptime, heap every
  5 min, setting numbers publish only on change.

Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>

screen_manager/app/updates.py

@@ -55,7 +55,7 @@ class Updater:
         return bool(self.task and not self.task.done())
 
     def screen(self, inbox):
-        return next((s for s in self.manager.inventory()[0] if s['id'] == inbox), None)
+        return self.manager.screen(inbox)
 
     def resolve(self, screen, profiles=None):
         """Profile file and OTA address for a screen; None when the add-on cannot tell."""
@@ -89,7 +89,7 @@ class Updater:
         # Callers that already hold the inventory and profile list pass them in; the inventory
         # handler otherwise re-reads every ESPHome profile several times per request.
         if screens is None:
-            screens = self.manager.inventory()[0]
+            screens = self.manager.screens()
         if profiles is None:
             profiles = self.manager.firmware.profile_names()
         return [s['id'] for s in screens