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.

extrahome/extrahome.go

@@ -0,0 +1,23 @@
+// Service extrahome provides extrahome APIs.
+package extrahome
+
+import (
+	"context"
+
+	"encore.dev/storage/sqldb"
+)
+
+var db = sqldb.NewDatabase("extrahome", sqldb.DatabaseConfig{
+	Migrations: "./migrations",
+})
+
+type StatusResponse struct {
+	Status string `json:"status"`
+}
+
+// Status reports whether the extrahome service is available.
+//
+//encore:api public method=GET path=/extrahome/status
+func Status(ctx context.Context) (*StatusResponse, error) {
+	return &StatusResponse{Status: "ok"}, nil
+}