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

By the way, people have already encountered the new version of the mod. They attacked giants, checked if there was a Golden Shot, attacked again, received a Golden Shot, and, accordingly, got beaten.

This could only have happened if they checked on the old version and attacked again on the new version. And that's the only way.

I didn't specify what the changes in the randomizer were, and all sorts of speculations started.
In essence, nothing has changed; there is only a difference with earlier versions – a different sequence of random numbers is simply chosen at the beginning of the battle, but it is still the same for the same battle.

Added 10 minutes ago

This suggests a ban on players saving games in principle. This is, of course, for online games. After all, nothing prevents a player from making a save beforehand, then checking something, and then, if something doesn't work out, disconnecting and thus returning to the initial state.

That makes sense.

After all, the presence of an opponent in battle can also be linked to a stopped, displayed opponent's timer.

If the opponent's timer has stopped (not at 00:00), then the opponent is in battle, and that's the only reason.
If it's ticking, then they are not. If a disconnect occurs during a battle, the timer will continue to be stopped; if it's not in battle, the timer will be ticking. If the opponent's timer does not appear when passing the turn, it means that they have not yet taken their turn.