feat(meetings): live invite, scheduling calendar, Discord-style redesign

- Live invite: ring a clinic member into a room (socket call:invite + a bell
  notification); the invitee gets a toast with a Join action. Notifications of
  type "meeting" deep-link to /messages/meetings?room=, which auto-joins.
- Scheduling: new scheduled_meetings table + /api/meetings/events (list mine,
  create, delete); a Calendar tab on the Meetings page with a month picker
  (meeting-day dots), the day's agenda, and a Schedule-meeting dialog
  (title/date/time/participants).
- Redesign: rounded control bar with tooltips (mic/cam/screen/invite + separated
  red Leave), speaking ring on tiles (Web Audio), and live room-occupancy counts
  via call:presence broadcasts. Migration 0025.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

frontend/lib/i18n/locales/en/translation.json

@@ -737,7 +737,34 @@
     "startVideo": "Start video",
     "stopVideo": "Stop video",
     "shareScreen": "Share screen",
-    "leave": "Leave call"
+    "leave": "Leave call",
+    "calendar": "Calendar",
+    "calendarEmpty": "No meetings on this day.",
+    "invite": {
+      "add": "Add people",
+      "title": "Invite to call",
+      "description": "Ring a team member into {{room}}.",
+      "search": "Search team…",
+      "noMembers": "No other members.",
+      "ring": "Ring",
+      "invited": "Invited",
+      "join": "Join",
+      "toastTitle": "{{name}} invited you to a call"
+    },
+    "schedule": {
+      "cta": "Schedule meeting",
+      "title": "Schedule a meeting",
+      "description": "Plan a meeting and invite your team.",
+      "titleLabel": "Title",
+      "titlePlaceholder": "e.g. Weekly sync",
+      "date": "Date",
+      "time": "Time",
+      "participants": "Participants",
+      "save": "Schedule",
+      "saving": "Scheduling…",
+      "failedTitle": "Couldn't schedule meeting",
+      "failedBody": "Please try again."
+    }
   },
   "messages": {
     "inbox": "Inbox",

frontend/lib/meetings.ts

@@ -35,3 +35,37 @@ export type CallPeer = {
   userId: string;
   userName: string;
 };
+
+// --- Scheduled meetings (calendar) -----------------------------------------
+
+export type ScheduledMeeting = {
+  id: string;
+  title: string;
+  date: string; // YYYY-MM-DD
+  time: string; // HH:mm
+  participants: string[];
+  participantNames: string[];
+  createdBy: string | null;
+};
+
+export function listMeetingEvents(): Promise<ScheduledMeeting[]> {
+  return apiFetch<ScheduledMeeting[]>("/api/meetings/events");
+}
+
+export function createMeetingEvent(input: {
+  title: string;
+  date: string;
+  time: string;
+  participants: string[];
+}): Promise<ScheduledMeeting> {
+  return apiFetch<ScheduledMeeting>("/api/meetings/events", {
+    method: "POST",
+    body: JSON.stringify(input),
+  });
+}
+
+export function deleteMeetingEvent(id: string): Promise<void> {
+  return apiFetch<void>(`/api/meetings/events/${encodeURIComponent(id)}`, {
+    method: "DELETE",
+  });
+}

frontend/lib/notifications.ts

@@ -39,6 +39,8 @@ export function notificationHref(n: Notification): string | null {
   switch (n.entityType) {
     case "conversation":
       return `/messages?conversation=${encodeURIComponent(n.entityId)}`;
+    case "meeting":
+      return `/messages/meetings?room=${encodeURIComponent(n.entityId)}`;
     case "patient":
       return `/patients?file=${encodeURIComponent(n.entityId)}`;
     default: