For some Nvidia GPUs, for example, you can use third-party tools to disable the HDMI audio sleep ... so your audio should be completely fine. A problem with this solution, particularly on Windows ...

Many monitors support audio over HDMI ... However, if they don’t, this post will help you resolve the problem when the HDMI playback device does not show up on Windows 11/10.

FIX: Windows Sound & Audio problems & issues. Sometimes ATI HDMI Audio device can be the reason for the audio popping out from your device; disabling the device ensures it is not the culprit.