Not sure about edge, but in my case vaultwarden autofill is working with vanadium, brave, ironfox...
Make sure u have set up bitwarden as prefered service in passwords, passkeys & accounts in settings.
Then in brave & vanadium (& maybe edge since chromium based?) go to settings > autofill services > autofill using another service.
Might be edge does not have the option to do this though, didn't test. If not, It might be an option to try to make perhaps another profile and install google play services, bitwarden and edge browser, set bitwarden in settings as prefered service, and this could maybe work.
It's been a while i researched this, but i believe remembering the default autofill option relies on some sort of google library. So if there's no option in edge to change it to another service, maybe above proposition might be beneficial to test.