Yeah, super-ugh. Every 2FA vendor wants to lock you in. I was able to export secrets from GAuthenticator on a rooted phone with sqlite, it looks like that is still possible on Authy too. Another vote for rooting your phone.
There 100% has to be a way for the user to own + backup their own private key material, or these are all just paths for stronger lockin.
Personally, I have a TOTP App (andOTP) with QRCodes on paper in cold storage, keepass-based tools for passwords across platforms, and Syncthing for syncing across these systems.
The closest you can currently get is an open-source authenticator implementation that lets you export its credentials, like e.g. Bitwarden does (it supposedly lets you export WebAuthN credentials via JSON, but I haven't tried it myself).
I get that any UI way to let users export credentials is a potential phishing/social engineering avenue, but the lock-in danger is real, and I'm holding back on WebAuthN as my primary authentication method for now.