UPD
I ran the 1.5.4 update and specified the Complete folder. HotA updated, other versions of Heroes didn't break; the question is resolved, but there is another one.
I click "Heroes TC". I select a mod, for example, "MoP Ride the Lighting". I click "Install mod". Something installs for quite a long time, but without errors. I click "Launch mod", and I see the following error:

The same happens with other mods in this section.