Heroes 5.5 WarGame Edition - Tactical Edition.

Temple Guard. They have machines, but no education. It's illogical; education should be a must-have for servants of the cult, and they are unlikely to be very good engineers (if you take medieval monks and priests as a basis).

In Age of Wonders 3, there is a class called "Theocrat," and the highest-tier unit there is the "Sanctuary of Punishment," which is a machine. The Theocrat class is quite close in spirit to the Temple Guard.
Other human classes are much less suited to machines, simply because there is nothing to discard.
By the way, the racial machine of humans (the one with a discount in the forge) is a tent.

Fanatics of faith don't necessarily need to be educated; in fact, faith often hinders education. Here, I followed the idea that the combination of education + magic is already common for most mages, so it's interesting to play with exceptions to this rule to avoid repetition. And of all the mages, the Temple Guard is the number one candidate for lacking education.
Besides, I proceeded from the fact that in the original game, education is not typical for humans (2% skill), and if the Temple Guard becomes educated, then humans will immediately have 2 out of 3 educated classes (in fact, one of the profile skills), and this is despite the fact that knowledge is only 10% for everyone!
In general, there are actually grounds both for an educated Temple Guard (because he is a wizard) and against an educated one (because he is a religious fanatic, and also with minimal knowledge). In one of the old versions, the Temple Guard had education (but not the Paladin).

Dark magic is also confusing, but I know about that author's concept, so I'll keep quiet.

I'm just consistent with the ideology that was established in the game, because I fundamentally don't want to change it; it's cool (Light + Dark). If the Temple Guard can't be dark, the Paladin can't be dark, and the Knight can only be dark by accident (he stumbled), then where does Light + Dark come into play?

I see a simple solution like this: no one said that magic without reference to elemental dragons is impossible. The corresponding hints of elemental affiliation of schools can simply be removed. Light magic = magic of blessings (for example, rename the "blessing" spell to "firm hand" or something like that). Dark magic = magic of curses. Chaos magic = elemental magic. There are no problems with summoning. The original mechanics of schools are preserved, and the lore is respected.

Maybe, but is it worth the effort? I even abandoned the old idea of renaming Chaos to Destruction and Summoning to Creation, because these terms are simply inconvenient to use.
In general, the mod was not intended to bring the game into line with the official lore; in this case, the convenience of the players is a higher priority, so I wouldn't want to disrupt it.
But as for the overall logic and conceptual integrity, i.e., the absence of contradictions and inconsistencies, I consider this aspect to be quite important.

Moving on to the heroes. Archmage. A good idea for a class with pure magic, but... It's still too harsh, with no combat skills at all. Will there be any bonuses to compensate?

The Archmage is the quintessence of a mage; combat skills are definitely not needed for him. Many magical schools have one problem: they don't enhance each other, because we only use one of the schools at a time, while combat skills can be combined. But this problem is solved by the "spell mastery" (+2x to magic) and "graduate" (+2x to knowledge) skills from the general racial education. By leveling up both skills and all 4 schools of magic, the Archmage can get +8/+8 to magic and knowledge for them, in addition to a wide range of spells. True, he will be without magic (it doesn't fit). Or with 3 schools with magic (+6/+6 from both skills). In any case, the Archmage already receives good bonuses to magic starting with 2 schools of magic (with education), and even more if he levels up new schools, because, unlike other classes, he can easily do this.

I think the Berserker has machines for no reason. He shouldn't have to think with his head.

The Berserker has machines because he is a gnome warrior, and engineering (machines) is a profile for gnomes (although defense is an even bigger profile). If you remove machines from the Berserker, engineering will become a useless skill that no race likes (and only 1 class out of 3 uses it).
In addition, if you give the Berserker leadership instead of engineering, then all the demons will fly to hell, because the demonologist will become too similar to the Berserker (5 skills out of 6 coincide).
Leadership is also bad for the Berserker, if you compare it with the Veteran. Gnomes have a pronounced patriarchy, hence leadership is only for Veterans.
Initially, the Berserker was called the Warlord; maybe it's worth returning to the old name?

Demonologist. I agree with the opinion above. In this word, the main thing is "log," it's a comrade with a claim to scholarship. He is not a leader, but rather a mage with a corresponding specialization. By the way, it would be logical if, by race, he was not an infernal. This is how it was in the new King's Bounty game, for example.

Here, perhaps, it is worth thinking about an alternative name that is suitable for a demon-fighter. I don't like the word "demonologist" because it contains the word "demon"; it's like putting an "elfologist" on elves.
Suggest other options.

Mistress. I find tying an entire class to a gender to be an unsuccessful decision. Who knows how the mod will develop further... You could have something like "overseer."

I definitely don't plan on more than 3 heroes per class. And even if new ones appear, almost half of the High Elf characters are female, so there shouldn't be any problems even in theory.
High Elves clearly have a matriarchy, so the ruling class is witches, priestesses of love, i.e., Malass. Hence, all 3 facial features of the class: magic (witchcraft), education (ruling class), leadership (charisma).