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You can, that's exactly what resident keys in this article is referring to.

Once all of those platforms have a more recent OpenSSH, you can ssh-add -K to add keys to your SSH agent.

I fully understand what kind of credentials FIDO2 can store - but as I read it this still requires manual configuration on individual devices.

Nope. It's in the article. Just insert the key and ssh-add -K. I wouldn't be surprised if other SSH agents (e.g. Apple) added a UI to do this.