KeepassXC is a good client that lets you handle your data how you want. I wrote a pro-Passkey blog post here[1] that explains how to do your own syncing, though I later discovered Passkeys are explicitly built to support proprietary software vendor lock in and had to revoke my support. If you are concerned about being able to control your own data outside of the big tech ecosystem, I strongly recommend avoiding passkeys entirely. It is possible for now, but they are not built for that and the spec authors are actively hostile to you managing your own data.
That is what I've noticed as well. The thread regarding KeePassXC is crazy... straight up threatening negative PR because KeePassXC allows people to store their private key, demanding that they instead take away user choice and modify their app to hide & prevent users from doing things. Passkeys appear to me to be nothing more than a corporate gimmick, and to be honest, I personally think in many instances they actually make you less secure... getting a fingerprint is way easier than making someone tell you their password. Now days the intelligence agencies likely already have your fingerprints as well.
I also meant to mention that many Keepass clients support Passkeys already today. Strongbox on iOS and macOS has similar or better integration to 1Password/BitWarden. Windows you probably want KeepassXC for now as it isn't fully baked in mainline Keepass. I don't know what you'd use on Android today, but I'm sure there's at least one and probably more on the way.
Bitwarden is free, and if you are concerned about these terms changing, the excellent self-hosted open source server implementation "vaultwarden" [1] supports passkeys as well.
