We’ve fixed this issue!

Starting with version 3.2.4 (it's live now! you can update the extension in Extensions -> Settings -> Check for Updates), audio should not be muted on any websites, and audio recording should work perfectly almost everywhere, including basically all video players.

Thanks for taking the time to write the review! It marginally prompted us to actually spend effort figuring out the issue, getting help from the community, and finally fixing it. That took hundreds of lines of code.