We use a home grown perl script for managing the process.
We're in the process of migrating from Asciidoc to AsciiDoctor because Asciidoc is no longer maintained. Asciidoc is also about 100x slower.
Either way, we convert the Asciidoc file to docbook and use Docbook to convert the docbook XML file into HTML. This is fairly time consuming because all of the docbook translations are implemented as XSLT. Which is slow. And soul crushing to extend of debug. So, eventually, we'll migrate from docbook to outputting HTML directly.
We use Parcel to wrangle our web resources.
It's pretty much the unix way: lots of little pieces all plugged together.
But we've spent a while customizing Asciidoctor to make it work how we need it to. It is nice to work with.
We looked at Antora and it looked great but it also looked time consuming to get from what we have to using it. Still, it is totally worth looking at.