feat: DM infrastructure overhaul + volume sliders + LiveKit dynamic URL

- Add DM edit/delete endpoints (REST + WebSocket)
- Add DM typing indicators with real-time broadcast
- Fix volume sliders to control LiveKit mic/speaker
- Fix Send Message button on user profile popout
- Add New DM modal with user search
- Fix message pagination (SQL cursor instead of in-memory)
- Guard optional attachments on DM messages
- Dynamic LiveKit URL from request Host header
- DM sidebar auto-sorts by most recent message

packages/web/src/api/client.ts

@@ -157,6 +157,10 @@ export const api = {
     },
     sendMessage: (id: string, data: CreateDmMessageRequest) =>
       request<DmMessageWithUser>('POST', `/dm/${id}/messages`, data),
+    updateMessage: (id: string, data: UpdateMessageRequest) =>
+      request<DmMessageWithUser>('PATCH', `/dm/messages/${id}`, data),
+    deleteMessage: (id: string) =>
+      request<{ success: boolean }>('DELETE', `/dm/messages/${id}`),
   },
 
   social: {