Initializes the WHIP client with screen sharing as the video source.
iOS: Starts the IPC server and shows the broadcast picker to the user. The user must select the broadcast extension to start screen recording.
Android: Creates the WHIP client, requests MediaProjection permission, and starts the foreground service. The user must grant permission via system dialog.
Initializes the WHIP client with camera as the video source. This should be called before connecting to the server.