Warlock – “Cultist” [Campaign 4, Mission 3]

Probably. I'm just quietly amazed by the difference in this mission on Hero and Veteran difficulties – on Veteran, it was a moderately easy walk, but on Hero, I'm dying in the first battles.

Yes, on lower difficulties, this mission wasn't the most difficult, but on Hero, it definitely is.

Chaos was only offered to me as a choice at the very end of the first mission, and I only managed to upgrade it once during the second mission – as a result, I never got to the Expert level. Also, the skill progression was very unsuccessful – I had to invest in defense, I never got Logistics, Education was offered only once, but I took the second level of Chaos, already getting tired of playing with Ice Golems. The only good thing was that I got Sorcery in the hut.

It was offered late, but it can be upgraded if you don't get distracted by side perks, except for something like Arcane Wave and Magic Attraction, and just upgrade the base skills. If you max out the other skills to Expert level, Chaos will definitely be offered for upgrade.
I didn't upgrade Logistics at all here, as the campaign is quite difficult due to the third mission, and it's better to invest in skills that will help directly in battle.

The problem is that I'm losing in the early battles. I did take the Castle – I had to spend mana and start attacking with Meteor Shower from the very beginning, but in the end, 40 Minotaurs and fifteen Assassins survived. Fortunately, it turned out that I was just "lucky" the first time with the enemy having 100 mana, the second time he didn't scare me as much and had a less intimidating reserve of 60, and also, the mana wasted on Phantoms, which didn't destroy anything except a single Beast, was a waste. But the very next day, a second blue hero arrives at the Castle with the same army, and I don't have enough mana or troops to defeat him.

Probably, I need to replay the second mission, as the hero's skills were developed very poorly.

Yes, the problem here is the not-so-successful skill progression. For this mission, you need Expert-level schools and level 5 spells, such as Earth Shock and Phoenix, if you're playing with summons. You also need Education with Magic Attraction; otherwise, you'll have a mana shortage. I had around 150 mana or a little less for the heroes, and even that was often only enough for one serious battle, after which I had to replenish it. And in general, Education is a very useful skill for a Necromancer, as it increases characteristics, especially the very important Sorcery skill. With a small amount of mana, underdeveloped skills, and a lack of high-level spells, I can hardly imagine how to complete this.
So, it's better to replay the campaign as Raileigh first. If necessary, you can watch on YouTube how others have completed it; there are videos from several very skilled players.