feat: Implement Matrix Rooms Bridge

- MATRIX_ROOMS_BRIDGE_SPEC.md documentation
- Migration 012: Add matrix_room_id/alias to city_rooms
- Matrix Gateway service (port 7025)
- City-service: auto-create Matrix rooms on room creation
- Backfill endpoint for existing rooms
- API returns matrix_room_id/alias in room responses

migrations/012_add_matrix_to_city_rooms.sql

@@ -0,0 +1,21 @@
+-- Migration 012: Add Matrix fields to city_rooms
+-- MATRIX ROOMS BRIDGE - link City Rooms to Matrix rooms
+
+-- Add Matrix room fields
+ALTER TABLE city_rooms
+  ADD COLUMN IF NOT EXISTS matrix_room_id TEXT,
+  ADD COLUMN IF NOT EXISTS matrix_room_alias TEXT;
+
+-- Create unique indexes (only for non-null values)
+CREATE UNIQUE INDEX IF NOT EXISTS city_rooms_matrix_room_id_uq
+  ON city_rooms (matrix_room_id)
+  WHERE matrix_room_id IS NOT NULL;
+
+CREATE UNIQUE INDEX IF NOT EXISTS city_rooms_matrix_room_alias_uq
+  ON city_rooms (matrix_room_alias)
+  WHERE matrix_room_alias IS NOT NULL;
+
+-- Add comments for documentation
+COMMENT ON COLUMN city_rooms.matrix_room_id IS 'Matrix room ID (e.g., !abc123:daarion.space)';
+COMMENT ON COLUMN city_rooms.matrix_room_alias IS 'Matrix room alias (e.g., #city_general:daarion.space)';
+