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I'll tell you what I did. I didn't really overthink it. I just copied the game folder to another logical drive (without deleting or changing anything).
(The game was on drive D, and I copied it to drive E).
Then, I simply ran patch 3.1 on the previously installed game (on drive D). Now everything is fine.
If I want to play version 3.1, I launch it from drive D.
If I want to play version 3.0, I launch it from drive E (i.e., the copy I made before installing patch 3.1).
The only thing is that now saves and replays are shared (for both versions) on drive C (in the documents folder).
Added after 4 hours 10 minutes
Regarding the change in balance in the game with neutral creatures... I haven't tested it much, but:
1. Version 3.0: For example, there was a battle - the hero (level 15, Orc) with four squads of level 1 units each defeated 25 Archmages (four squads). The AI was acting stupidly when it shouldn't have - casting punishing strike and other spells.
In version 3.1, the same hero, the outcome of the battle is the same - victory over the mages (isn't that ridiculous - 4 units of level 1 can defeat 25 archmages, but the hero has a machine gun and spells :p).
2. Second case - in version 3.0, four squads of level 1 units defeat 4 squads of Cavern Crawlers (mages) - a total of 22. My losses - 1 unit. The Cavern Crawlers are doing stupid things - for example, casting a destructive beam.
But in version 3.1, this trick no longer works - because they immediately attack with a fireball!
It turns out that they slightly adjusted the balance of the battle with neutral creatures, so it will be more fun to play!