Fortunately for me, I've not had to deal with this, but I have used Jack. Jack is an audio tool that you can use to pipe audio from one application to another (think "jack" as in "audio jack"). It might possibly useful for managing the audio so that it goes directly from the Zoom output into the recording application, bypassing your speakers.
A web search for "
record lecture linux" will turn up a number of articles and tutorials you might find helpful.
I see no reason why you couldn't record on one workspace while doing something else on another workspace, but it is likely wise not to attempt to play music while recording a screencast, but I've never tested that. I would suggesting testing your setup with some YouTube videos or streaming video, say from tubi.tv or some other streaming service.
Just a few thoughts off the top of my head.