Look up passkey provider attestation. Services can't block your password manager, but they can block your passkey manager. It was used to threaten the KeePassXC devs into removing cleartext passkey exports.
Services manage to "block" my password manager all the time by confusing it to the point where I have to copy and paste my password manually. It's a huge security risk (because where am I actually pasting this password?), and super frustrating.
EDIT: I'm not saying that the passkey situation is great, but it's not worse than passwords. It has so many benefits over passwords that we should absolutely not let perfection be the enemy of good enough!
That's incorrect. There is nothing in a passkey that identifies it as a "key from KeePassXC", so it can't be blocked.
BitWarden exports passkeys just fine as cleartext, or to be precise as a file encrypted by the user-specified passphrase. So you can then decrypt it at your leisure.
While I don't agree with the grandparent's fears, you're only half correct: The server can mandate that you use an authenticator from X company, so some sites might block KeepassXC, even if they don't block a specific key.
EDIT: I'm not saying that the passkey situation is great, but it's not worse than passwords. It has so many benefits over passwords that we should absolutely not let perfection be the enemy of good enough!