perf(P6A.T5): pre-warm Supabase + avatar loading hints

Fire a no-await profiles query in AuthContext on session establish to absorb
cold-connection latency before the first user-triggered request. Add
loading='lazy' default to the central Avatar component so all off-screen
avatars (chat list, friends list, popovers, message senders) skip eager
Supabase Storage fetches; set loading='eager' on ConversationHeader (active
conv header) and CallParticipantTile inline imgs (both AudioContent and
VideoStub) which are always above-the-fold when visible.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

apps/desktop/src/context/AuthContext.tsx

@@ -204,6 +204,14 @@ export function AuthProvider({ children }: { children: ReactNode }) {
     void registerWebPush(installId);
   }, [session]);
 
+  // Pre-warm Supabase: fires the first round-trip in the background so the
+  // first user-triggered query (e.g. loading conversations) doesn't pay
+  // the cold-connection latency.
+  useEffect(() => {
+    if (!session) return;
+    void supabase.from('profiles').select('id').limit(1).then(() => undefined);
+  }, [session]);
+
   // Phase 3: ensure this install owns exactly one devices row. The row is
   // pure session-list telemetry — it does not carry any cryptographic
   // material since the per-user-key refactor. We re-use the row across