I received a mail from RT pointing to https://about.readthedocs.com/blog/2024/07/addons-by-default/ and explaining that ptb currenlty relies on html_baseurl and that it should be set via

import os
# Set canonical URL from the Read the Docs Domain
html_baseurl = os.environ.get("READTHEDOCS_CANONICAL_URL", "")
# Tell Jinja2 templates the build is running on Read the Docs
if os.environ.get("READTHEDOCS", "") == "True":
    html_context["READTHEDOCS"] = True

This is also explained somewhat in the current docs

Additional changes may be needed to adapt to RTD addons - in particular they include a native search as you type addon. I'll create a spearate issue for that and link to the furo theme issue tracking the topic.