I went from Zoom to Jitsi with my family, because I was tired of it pushing the desktop client to me and the webapp limitations as you point out. Jitsi web supports Grid view, as well as desktop sharing (with audio!). We've been playing Jackbox games over it just fine.
Right in Jitsi, you share your screen and Chrome's dialog opens, you go "application window" and select your game, and check the little box "share audio". Here's a GIF from their newest blog post showing it: https://335wvf48o1332cksy23mw1pj-wpengine.netdna-ssl.com/wp-...
