feat(ui): show toast notification for new join requests

When a join request arrives via WebSocket live event, display a toast
prompting the user to review it in the inbox.

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

ui/src/context/LiveUpdatesProvider.tsx

@@ -227,6 +227,29 @@ function buildActivityToast(
   };
 }
 
+function buildJoinRequestToast(
+  payload: Record<string, unknown>,
+): ToastInput | null {
+  const entityType = readString(payload.entityType);
+  const action = readString(payload.action);
+  const entityId = readString(payload.entityId);
+  const details = readRecord(payload.details);
+
+  if (entityType !== "join_request" || !action || !entityId) return null;
+  if (action !== "join.requested" && action !== "join.request_replayed") return null;
+
+  const requestType = readString(details?.requestType);
+  const label = requestType === "agent" ? "Agent" : "Someone";
+
+  return {
+    title: `${label} wants to join`,
+    body: "A new join request is waiting for approval.",
+    tone: "info",
+    action: { label: "View inbox", href: "/inbox/new" },
+    dedupeKey: `join-request:${entityId}`,
+  };
+}
+
 function buildAgentStatusToast(
   payload: Record<string, unknown>,
   nameOf: (id: string) => string | null,
@@ -461,7 +484,9 @@ function handleLiveEvent(
   if (event.type === "activity.logged") {
     invalidateActivityQueries(queryClient, expectedCompanyId, payload);
     const action = readString(payload.action);
-    const toast = buildActivityToast(queryClient, expectedCompanyId, payload);
+    const toast =
+      buildActivityToast(queryClient, expectedCompanyId, payload) ??
+      buildJoinRequestToast(payload);
     if (toast) gatedPushToast(gate, pushToast, `activity:${action ?? "unknown"}`, toast);
   }
 }