Send the trimmed snapshot to the watch over WatchConnectivity

App Groups are per-device, so the watch cannot read the file the phone writes
and has to be handed the data. Three delivery paths: application context for
the latest state, a complication push only when the next appointment actually
changed (the budget is small), and a reply to the watch asking directly.

Sign-out pushes an empty signed-out snapshot. Clearing our own container is not
enough — the watch holds its own copy and would keep rendering the previous
user's calendar.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

Calendarr iOS/CalendarrApp.swift

@@ -8,6 +8,7 @@ struct CalendarrApp: App {
         // Registration has to happen before the app finishes launching, which
         // is why it is here and not in a .task modifier.
         BackgroundRefresh.register()
+        WatchSyncService.shared.activate()
     }
 
     var body: some Scene {
@@ -114,6 +115,9 @@ class AppState {
         // say "sign in to Calendarr" rather than "open Calendarr once".
         WidgetStore.clear()
         publishSession()
+        // The watch keeps its own copy of the snapshot, so clearing ours is not
+        // enough — it has to be told, or it keeps rendering this user's events.
+        WatchSyncService.shared.pushSignedOut()
     }
 
     func resetServer() {