I got confirmation from apple developer accelerator. When the Background Modes are Audio, AirPlay, and Picture in Picture, it is not possible to update the Live Acitvity.

This is not a good way to solve the problem. Modifying this will cause the volume of the app to be affected by the mute button.

This is an online lecture, and no screen recording is allowed, so I cannot give evidence accordingly. This online campaign is from Apple Developer Relations - Apple China Design Development Accelerator.