Sorry, I can understand that you’re upset about your situation.
But providing your 2FA (or 2FA recovery code) would be the way to prove you are really you. And it’s up to you to make sure you don’t lose those login credentials – as it’s also written in Bitwarden’s Terms of Service - Account terms:
And you can still access all your data, as you logged in there while you – obviously – still were able to log in there. As long as you use an unlock method, then you remain logged in there. But when you now lost your second factor, of course you can’t log in without that now on “new” BW clients/apps.
But losing your second factor alone – fortunately – doesn’t automatically log you out on the BW clients/apps where you’re still logged in.
Honestly, I think you should consider yourself lucky that you still have access to your data at the moment. Consider this: if you were not logged in in any BW app when you lost your second factor, then you had no access at all now. Would you be happier if it were like this now??
BTW, I agree (again) with @grb – as an organization/collections are involved, you should contact BW support for further guidance how to handle that part.