Is this webcam compatible with a game console(PS4 /PS5/XBox)?”
Unfortunately, it is not. PS4/PS5 does not allow 3rd parties cam
You’ll need a webcam that has a YUY2 or NV12 format to broadcast with it. AVerMedia Live Streamer CAM313 has this format. On the other hand, Live Streamer CAM513 has the default MJPEG format so there's an Audio IC compatibility behavior. There is a potential solution for creators on Xbox with CAM513+AM310(URL: https://www.avermedia.com/us/product-detail/AM310). Both of them could work together on Xbox for streaming.