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

Are you talking about the fixes?

The HD mod changes the file names of random maps from the standard "random_map_0.h3m" to new names like: "Ivor_vs_Computer_0.h3m", or something similar.
If this feature can be disabled, then to run the mirror under HD, a modified executable of WoTA is sufficient.

And the quick troop operations are also very inconvenient in WoTA after HD. Is it possible to implement HD-style in WoTA?

I think it's more a matter of habit. For people who don't play on SoD+HD, such a change would be inconvenient instead.
I don't know what the significant differences are between the HD and WoTA interfaces, but if HD has some actually useful features that are missing in WoTA, then why not add them. But this is up to Asmodeus.
Besides, questions or suggestions about WoTA or the symmetrical template should be posted in the corresponding topics.

Yes, that's the simplest solution. It would also be good to add information about whether a unit has waited, and the number of the current round.

Information about wait times is already available in the log, so if it is to be duplicated, it would be desirable to do so not in the info window, but directly on the stack image.
And the round number can be indicated in the log.