I've been using Authy for TOTP in conjunction with Bitwarden Premium for passwords.
I considered using Bitwarden Premium for TOTP, but dislike having passwords and TOTP codes in a single-point-of-failure backup location.
I looked into Bitwarden Authenticator, but it didn't seem to support sync between devices, as you've now corroborated. This is the reason I gave up on Google Authenticator and switched to Authy — I don't want to have to deal with trying to get all my accounts unlocked if my phone gets lost, broken, or stolen.
I've set up Authy with a backup password so that I can recover it if necessary. I understand that this is less secure, and Twilio (the company behind Authy) seems to have a mixed reputation. However my reasoning is that maintaining two layers which are separate (Authy on phone and tablet, Bitwarden on laptop) is consistent with defense-in-depth theory — even if the layers have some weaknesses.
Maybe it's time to switch to Yubikey, because TOTP apps that don't sync between devices are too high of a risk for losing access, and TOTP apps that sync aren't quite "something you have". How do people prepare for the potential loss of Yubikeys? Is it reasonable to get a spare[1] and keep it in a safety deposit box?
[1] https://www.yubico.com/products/spare/