Not really an alternative, since C++ projects often use Breathe to "transpile" Doxygen to Sphinx. I even contributed a few patches to Doxygen from which the Breathe/Sphinx project directly benefited, but after trying it out a bit and hitting a few walls, I realized I would achieve better flexibility by having my own frontend.

Especially because (if I can dare to say) I ended up with a much better search than what Sphinx (or Doxygen) has -- try it out: https://doc.magnum.graphics/magnum/?q=max#search ;)

Yes, the search functionality in Sphinx leaves a lot to be desired, even if you are already writing your own Sphinx plugin it is fairly difficult to add stuff to the search indices in a meaningful way. It's also slow. Overall Sphinx suffers a lot from hardcoding the reST data model and directly working with that.

You don't have to use Doxygen with Sphinx although you can.

The DPDK documentation uses Sphinx, and it's great. For a massive codebase like that, it's a nice addition compared to what an IDE would do.