Separate 2FA OTP app from my password manager

Do you think it's worth keeping 2FA OTPs in a separate source from your password manager? Currently I keep them in Bitwarden. I was thinking keeping them separate could add a little extra security in case my BW was cracked, but not sure it's worth the hassle of loading a second app for logins.

Do you know of an app that does 2FAs as conveniently as Bitwarden, in that it has mobile apps, browser extension, etc that can all access the same vault?

here's one i came across from an awesome-selfhosted list. i would need to test the PWA experience https://github.com/Bubka/2FAuth