For me it depends how “hardened” the account needs to be.
For key accounts I keep the 2fa seperated (where possible with a fido token) For not so relevant accounts I add it to bitwarden. Because I probably wouldnt activate 2fa for these accounts if I’d have to pull out the phone each time
Edit: you also can add the 2fa token to a separate vault
For me it gets a bit confused if I add or remove the external screens.
Usually it is fixed if I quit and restart flameshot