@martijn has shared his similar troubles: https://community.wolfram.com/groups/-/m/t/2214983
I leave a remark here because the issues are clearly from the outdated Workbench.
I have contacted WRI, and they confirmed the issues. They say that the developers are working on a fix and a new public version of Workbench is coming sooner or later. Well, it was about a month ago.
What I noticed was that the documentation pallet was not available in
12.2 unless I started Mathematica from eclips and the errors pointed to the lack of these tools. In the MathematicaSources of workbench the
DocumentationTools and DocumentationBuild were present.
I didn't dare put the resources from Workbench distribution to the system installation directory. In fact, I am doing the opposite. I use DocumentationTools coming from Mathematica 12.2, which looks better and easier to launch even without Eclipse/Workbench, to edit my documentation files. Then, I build them using Eclipse/Workbench.
My Workbench version, which I obtained directly from WRI, is slightly higher than the public version. It is still outdated and problematic. It just builds my documentation files -- I cannot even edit my files within it.
There is DocumentationBuild as a sub-package of PacletTools of Mathematica 12.2. I was thinking of directly -- without Workbench -- using it to build my documentation. No luck yet.
As it is, making integrated documentation is too much of a headache, at least, for the moment. I have an impression from Mathematica 12.2 that they are trying improve it by integrating the required tools right into the system. I hope this transition period ends soon.