The latest version (4.31.0) works. In fact, it is the tool I mentioned that I tested outside of Traefik.
According to the go-acme changelog, they added the new API in version 4.27.0, and Traefik 3.6.6 uses version 4.30.1. Traefik is only one version behind go-acme, and the changelog does not indicate that any relevant changes have been made regarding the Hetzner API.
We will wait for Traefik to update to the very latest version of go-acme, but honestly, it seems strange to me. Thanks.