Storing 2FA codes is just the beginning. Bitwarden aims to add defense in depth to authentication.
Bitwarden Authenticator is a standalone app that is available for everyone, even non-Bitwarden customers.
In its current release, Bitwarden Authenticator generates time-based one-time passwords (TOTP) for users who want to add an extra layer of 2FA security to their logins.
There is a comprehensive roadmap planned with additional functionality.
You can use Authenticator Pro (android, opensesource) and Proton Pass, both let you copy the TOTP generation code to paste into another without problem. Both generate exact code
In fact that's how I am using them right now, with Authenticator Pro is my on-device, offline, encrypted backup offline backup TOTP for Pass.
I guess it is not as straight forward as export import as you hope, but it's not as bad as other options used to be.
As long as you can access the keys, you can swap authenticator apps.
I tried a few until I landed in Aegis, and I have two on my desktop that I'm trying out as well. Just get something that allows exporting the keys and there will be a path to switching apps.