KeepassXC lets you export the private key, which you can then back up or import into another KeepassXC instance. I have tested this, it works. I even shipped my exported private key off to a friend in another state and he was able to import it into a KeepassXC instance and log in to my account. Presumably another password manager could support importing the data, as it's just plaintext, though I don't know if any do.

Unfortunately the spec authors think this export feature violates the spec and have threatened KeepassXC with being banned by authenticating websites[1]. This explicit support from the spec authors for client banning makes passkeys non-viable to me. The websites I log in to should not be able to restrict what clients I choose to use to manage my own data.

[1] Spec author writes, "To be very honest here, you risk having KeePassXC blocked by relying parties. ... (RPs [may] block you, something that I have previously rallied against but rethinking as of late because of these situations)." https://github.com/keepassxreboot/keepassxc/issues/10407

Just having the data exported is peace of mind for me. It's trivial to import or convert to another format (even if not implemented now), so the worst-case scenario is acceptable, especially considering how much better Bitwarden + Passkeys are to every other form of authentication.

BitWarden is OpenSource. I did try importing the export using my own hosted BitWarden server, it worked.