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

Pressing the Q key ends the battle with a quick battle.

I conducted research on quick battles and auto-battles.
Different results when pressing Q at different times – this is solely due to the hero's random behavior (I verified this by making the random number generation function return the same number).
It has also been established that different obstacles are set up on the battlefield during a quick battle and during a subsequent replay – this is also due to the hero's random behavior.
That is, when generating the same number using the aforementioned function,
the results of the quick battle and the replay with pressing Q before and after the pre-battle music finishes are absolutely identical, and these results are not affected by restarts or anything else.
However, the auto-battle, despite the bug fix regarding flying creatures in the quick battle, still differs from the quick battle.
For example, in a save with Myrlan and 1,000 griffins,
in the quick battle, the first stack of griffins makes a move, while in the auto-battle, they wait.
But this does not mean that creatures do not wait in the quick battle. They do wait, but differently, i.e., different stacks wait at different times. In general, the battle is fought differently. Judging by the example with Myrlan and 1,000 griffins, it seems that Myrlan fights 'smarter' or the griffins are 'dumber' in the quick battle than in the auto-battle. But what exactly is the reason – who knows.
Maybe Sav will figure it out...