Include join requests in inbox badge and auto-refresh via push

The sidebar badge count was missing join requests from its inbox total,
and the live updates provider had no handler for join_request entity
type, so new join requests wouldn't appear until manual page refresh.

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

ui/src/context/LiveUpdatesProvider.tsx

@@ -369,6 +369,11 @@ function invalidateActivityQueries(
     return;
   }
 
+  if (entityType === "join_request") {
+    queryClient.invalidateQueries({ queryKey: queryKeys.access.joinRequests(companyId) });
+    return;
+  }
+
   if (entityType === "cost_event") {
     queryClient.invalidateQueries({ queryKey: queryKeys.costs(companyId) });
     return;