Adapt to RTD Addons

Start by checking Furo issue #795 and the Read the Docs Addons guidance, then inspect the type-as-you-search implementation and the referenced lines in .readthedocs.yml. Test the RTD build and confirm whether search still works and whether the existing configuration is still needed, including compatibility handling if required.

Apart from the changes in #4386, some additional changes might be necessary to adapt to RTD Addons once our furo theme has adapted. Punshlines:

• the switch needs to happen by 2024-10-07
• furo tracks the transition in https://github.com/pradyunsg/furo/issues/795. I've already subscribed to that thread.

I recommend that we wait for the issue to be closed and then test out what we need to change. In particular I expect that we might need to

• check if our type-as-you-search implementation still works and if we can replace it by the new native feature
• Check if this part of our rtd build still works/is still needed

If furo is ready before 2024-10-07 I recommend that we try switching early

If furo is not ready at 2024-10-07, we should try (preferably a bit before) to use sphinx-build-compatiblity to manually enable backward compatibility. Or at least check if that's necessary.