What apps you have installed that are present on both your W10 and W11? Considering your symptoms and the variables I would wager it's a third party app that conflicts with steam. I would try to clean some of these applications or all, and launch steam and the game in a different compatibility mode.
As a last resort, uninstall the game on both PC's, uninstall steam on both, cleanup your AppData/local/ files on both PCs. There are some cache files for BG3 and steam here which might conflict and if you play from two devices but use same account some that are corrupt might be shared.
Then install steam and the game on only one PC. And create a new profile see if it still happens.
