I’ve just been contacted by the Thomas Gazagnaire (the dune-release maintainer) to discuss the recent problems. Strangely, when trying to replicate the problems to provide more details, it turned out that both the *.descr linting issue as well as the documentation publication issue have disappeared. Since even older dune-release versions don’t exhibit the issues anymore, I suspect that either used libraries or tools may have been responsible.
Anyway, the gist is that you can apparently follow the simpler release process outlined in Experience report switching to jbuilder and topkg, replacing topkg with dune-release. Just keep the above hints in mind in case the mentioned problems still bubble up with your installation.