That's exactly the issue I have with passkeys. All that lockin to big tech. I tried bit warden but most sites with passkeys didn't work with it (like Amazon and PayPal). And on android it only wants to use the Google version (I don't use a Google account on my phone so that's not possible).
Bitwarden works just fine for Amazon. Works on my phone too. Even when supplying passkeys over QR code+Bluetooth to another computer, Bitwarden's Android integration works flawlessly.
I do believe you need Android 14 for that, though, so if your phone has been abandoned by its manufacturer/your ROM of choice, it'll break.
If Bitwarden is bugged out on your computer/phone for whatever reason, there are also alternatives like 1Password.
None of what you wrote is true though, is it?
Amazon, PayPal work just fine on my 3rd party 1Password extension. And it works just fine on Android as a default passkey provider as well.