I also keep my 2FAs in my password manager vault.

Unless your dedicated 2FA app is on a separate device, it's not really acting like a second factor anyway. I.e., if your device where your Bitwarden vault is compromised, a separate 2FA app on the same device means your 2FA could still be compromised.

It's still worthwhile to have the 2FA enabled for other reasons though.

If you need something just for Bitwarden, then maybe consider a hardware device like YubiKey?