feat(videochat): implement LiveKit integration for video chat functionality

- Add LiveKit client setup and token generation for room access.
- Implement room management functions including CreateRoom, OpenRoom, ListRooms, and DeleteRoom.
- Introduce participant management with ListParticipants and RemoveParticipant functions.
- Create tests for room and participant management, ensuring proper authentication and authorization.
- Add error handling for LiveKit API interactions.
- Define data structures for room metadata and token responses.
- Implement status endpoint for service availability check.

profiles/migrations/11_personal_setup.up.sql

@@ -0,0 +1,9 @@
+CREATE TABLE personal_setup (
+    user_id UUID PRIMARY KEY REFERENCES user_profiles (user_id) ON DELETE CASCADE,
+    can_broadcast BOOLEAN NOT NULL DEFAULT FALSE,
+    room_name TEXT NOT NULL DEFAULT '',
+    CONSTRAINT personal_setup_broadcast_room_check CHECK (
+        (NOT can_broadcast AND room_name = '') OR
+        (can_broadcast AND octet_length(room_name) BETWEEN 1 AND 128 AND btrim(room_name) <> '')
+    )
+);