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

I'm a little tired of the routine of translating HD to a new platform...

Let it be a pleasant fatigue :)
As for the new features:

...
- continuous display of the remaining time for a turn in the format (hh:)mm:ss, regardless of which window is active (even the message window).
(I'm basically just a step away from implementing a chess timer)...

This is a very useful addition. Perhaps, display the timer (numbers - hh:mm:ss) outside the game field and/or make them stand out enough against the background) and, say, with sound accompaniment - if 3/2/1 minutes remain, play a triple/double/single beep.
By the way, now, with parallel sound settings, these very system sounds often disappear (are not heard), which is not very good.

- start the turn timer after clicking "OK" in the message preceding the turn.

This is a very important decision, especially when you need to run to the store during your opponent's turn:cool:

- a wider choice of turn duration (I don't know how to do it: you can set any time from 1 to ?, or you can simply add 3 minutes)

You can set 3 and 5 minutes. Just in case there are chess clocks someday, you can set seconds there.
And another point about the turn timer. When you take Pandora in the last seconds of your turn, you simply don't have time to figure out its contents. If Pandora gives experience, there is no way to choose the right skills, and if it gives troops, they may disappear. So, can it be done so that such operations are still carried out in accordance with the player's will, and not the timer?

- alliance selection with a user-friendly interface in the original style.

This will undoubtedly save time in paired games. By the way, a remark about the autosave right away. In a 2x2 game, the save has a very long name, and when loading, you can't see its end (game day) and the file extension. Therefore, it would be more convenient (in a game with more than 2 players) to have 3 letters from each player's name in the record.

I don't know if it's necessary: - you can increase the waiting time for a response from the player, after which the game writes: has left the game (you have become the server), you can add a dialog box with the question: unable to..., try again?

It's not quite clear what the advantages of this are. But the fact that the system always writes that some other player crashed when there is a crash, but not you yourself (even if you are actually the one who crashed), is strange.

p.s. there was also a suggestion to provide artifacts on the map with a caption with their self-name, and not just a "Artifact" label. I can't say whether this is a bug or it was intended. But very often artifacts are hidden by terrain or objects, and it's hard to guess.
... and quick exchange of troops in the garrisons of cities and mines:)
In general, we are waiting for testing...