Hey so i haven't tried the vr strip chat, however this should work just fine using a virtual desktop app (my thinking is, if i can pull up and pin windows from my desktop to my cockpit in elite dangerous there's not reason it should work for anything else) --did a quick look and yes it quest 2 can run virtual desktop, you will need a vr ready pc and you will need to buy the quest version of virtual desktop (through the quest store) the streaming app and a copy of the quest downloaded to your desktop
https://www.vrdesktop.net/ full information can be found there. There are better options (for anyone else coming across this) for every other vr set , ovrdrop or ovr toolkit. (apparently you can get ovr toolkit working with quest but you also need quest link and pro vr and its not as contestant oas on other devices. So while untested i should be possible to from your vr chat throw open a browser window (or have one pinned) that has your settings. Now whether the changed settings and the redrawing of your environment would maintain its connection, not sure. But it should.