I know how to make a unit unique using the UnitClassInfo file. But units like Bersekers or Apothecaries don't appear there. Is there a simple way to make them available to everyone?

The reason UU and UB are "Unique" is because they share the same Building class with another building. For example the Berserker is UNITCLASS_MACEMAN and UNIT_BERSERKER

To make it, non-unique, you have to add it as its own UNITCLASS.

For example UNITCLASS_BERSERKER, in the UnitClassInfo file.
Then in the UnitInfo file, give the berserker entry, this new class, replacing the maceman class, and it should work.

Thanks, edgecrusher! Worked perfectly!