If it's magic link or multi-factor authentication, I know which one I prefer. Try explaining to an MFA-loving service that your phone is out of action while it's being repaired.
I don't understand your point. This is exactly what multi-factor authentication protects against if you don't store your MFA codes in your password manager.
standard TOTP MFA (which is what most password managers would offer in terms of MFA) uses a shared secret, which you would just dump from the same database you get the dumped passwords from.
unless you use asymmetric crypto e.g. in webauthn this doesn't benefit you at all.
If your concern is phishing, storing the code on the device (especially on a modern phone) is really moot since all forms of one-time codes are vulnerable — you should be working on how to switch to FIDO2/WebAuthn.
If your concern is a temporary exploit of the user's browser, using an out-of-process password manager is likely to prevent exfiltration of the entire password list but in practice this is already probably a disaster scenario unless you're using sites which require a strong FIDO2 challenge for sensitive operations since the attacker already has your cookies for everything you use regularly.
Storing them in Bitwarden is more convenient by far, but storing TOTP is a paid feature.
It slightly raises the risk in the scenario where your password vault gets hacked, but like with putting all your passwords in the same place, if you've only got 1 place to protect it becomes easier to protect it more thoroughly.
I came to grips with the idea that I really don't care all that much if a single factor has risks as long as the other factors have orthogonal lists.
1. Use my Yubikey with a different phone via NFC or a different computer using USB 2. Login using my other iPhone or Mac because the WebAuthn passkey is synced via iCloud (this is in the progress of coming to Chrome & Windows)
The nice thing is that all of those are more convenient than using email in addition to being more secure.