HoMM3 HD is a mod (add-on) for the game Heroes of Might and Magic 3.

if anyone else encounters this problem.
The issue was with the HotA version. Currently, different resources have different HotA versions, and there isn't one definitive, up-to-date version. Some have 1.36, 1.38, 1.38.2, or 1.40. Basically, you can install them all at once and switch between them depending on the "requirements" of your opponent.
Thanks to everyone who helped with advice.