Is it possible to use WebAuthn for digitally signing documents in the browser?

WebAuthn is a relatively new API for authentication, and it uses public key cryptography instead of something like passwords.

I am wondering if it is possible to use the cryptographic part for a different purpose, specifically creating digital signatures of documents in the browser.

The idea is to find a way to have a user sign a document in the browser in a way that the server can’t fake or manipulate. So the web application itself must never know the private key that is used for signing, which is the case for WebAuthn as far as I understand.

So if instead of the random challenge that WebAuthn expects I’d send the contents of a document I want the user to sign, I should get back a cryptographically signed hash of my document, if I understand the explanation on MDN correctly.

In the end I should have a digital signature that could be used to prove that this document was signed by a specific private key from a specific hardware token. And neither the web application inside the browser nor the server component ever saw the private key, and can’t fake this signature (of course the application could compromise this by switching out the content before signing, but not later).

I couldn’t find anything on someone using WebAuthn for this purpose, and anything I could find related to digital signatures in the browser was about stuff like Java applets that is simply not an option today anymore.

Is my idea sound in general? Or am I misunderstanding how WebAuthn works and it’s simply not possible to use it in this way? Are there any weaknesses or flaws in this approach that I’m missing?