The enhanced battle against Markel is more like a micro-fix; in the original, if you kill the main undead, the summoned creatures disappear, and the battle ends very quickly. Otherwise, you have to finish off all the summoned undead, as in the final mission.
Essentially, yes, 99.9% of them are similar to the original missions, except that there are units from Tribes of the East. I think the third tier doesn't hinder gameplay; it's just a game mechanic. No one prevents you from playing without the third tier if you want, like in the original.
In short, it's best to see and play it yourself.

Yes, the 3rd tier isn't a problem; in the "OldCampaign" mod, not the remaster, there's also a 3rd tier. I've always just ignored it; it's not difficult. And the fact that there are units from Tribes of the East on the map... well, let's consider it a "reasonable price to pay for the ability to play the original and Hammers of Fate campaigns in Tribes of the East" :D. Markel, let's say, makes sense; overall, it sounds logical. But I would like to remove the enhancement of ordinary original battles with many enemy heroes and the transfer of artifacts, if possible. I understand that this is your mod, and you want it to be this way, so I'm not asking you to change anything in your mod for me. Rather, I'm asking you to tell me, if it's not difficult, what exactly and where I need to change in the mod files to remove these innovations? At least briefly, and I'll figure out the rest myself :D.

As for the "third tier in the original and Hammers of Fate," it's not just about that. I even made a text file for myself with a reminder of what exactly wasn't in Heroes 5 original and Hammers of Fate, and what shouldn't be used :D. If you need it, here's the list:
You can play the mod for the campaigns from "original" + "Hammers of Fate" either by using all the innovations of the "Tribes of the East" add-on, or
by limiting yourself and not using the new mechanics that can give a clear advantage. If you need to know what exactly wasn't
in "Tribes of the East" or "Hammers of Fate," here's a list of the most important (not all) changes that can significantly
affect the balance:
1) New race - Stronghold (before ToE), Fortress (before HoF). And, accordingly, the heroes of these factions and all their units.
2) New alternative tier of creatures (before ToE), 3rd option (2nd improved).
3) The ability to hire a caravan to transport creatures from buildings on the map to your city (before HoF).
4) New spells (before ToE): magic of light - regeneration (level 2), divine vengeance (level 4); magic of darkness - sorrow (level 1), vampirism (level 5);
magic of chaos - stopping chill (level 5); magic of summoning - crystal secret (level 2), wall of swords (level 3), summon hive (level 4).
5) Selling artifacts on the market in the city (before ToE).
6) New buildings on the map (before ToE) - mentor, sacrificial altar, library of spells, astrologer's tower.
Conclusion: I only included the biggest changes that can significantly change/make the game easier, and which are easy to avoid during the game. Of course,
there were many more changes in the add-ons, but I considered the others to be either not important enough, or something that is extremely difficult (and in some places
even stupid or impossible) to avoid.