I think that it is a board issue. As your board does power conversion, D/A conversion and amplification, I guess somewhere it picks up some static noise that get amplified even when the Pi is not providing an I2S signal.
Easiest way to test I think is to turn on your Pi without the SD card so it doesn’t boot anything. If than you already hear the noise, it is not the Pi.
I agree with PatrickB. I own this board, and I would add that it’s sensitive to the electrical environment. Power cable near the board may cause this.
Take care the power supply cable does not touch the board.