After looking into the code of your next integration it seems that the new version is using the old useRouter hook that comes from next/router, but it should be using the hooks from next/navigation (Next documentation).
Thank you for the answer, Priyanka. I understand that the support is not 100%, but the thing is that in the Prismic documentation it says that we should use the 1.x version of @prismicio/next to get the support for Next@13, but it uses the things that wil break in Next@13.x. It seems like a bug and I didn't find a post about it anywhere.