Silly computer, can we get a fix?

As I see, you didn't just come here to theorize.

The developments of vcmi might be useful:
https://github.com/vcmi/vcmi
They are developing an engine with open source code.

Website: http://forum.vcmi.eu/portal.php
Bug tracker: http://bugs.vcmi.eu/my_view_page.php
Unofficial daily builds for Windows: http://vcmi.arseniyshestakov.com/windows/

It is planned to be cross-platform. There are versions for Windows, Linux, and Mac. Someone from the community compiled it for Android, but it hasn't been updated for a very long time and is hopelessly outdated.
The version is still raw, with a large number of bugs, it's basically a deep alpha. And one of the main drawbacks is that the AI is even weaker than in Heroes 3.
I'm helping a bit with testing as a player. Usually, these are minor, obvious bugs. Personally, my goal is to see a competitive AI. Well, maybe not competitive, but at least not as idiotic as in the original. Therefore, personally, I am all for such an idea.

Added 1 hour 51 minutes ago

Secondly, playing chess against a computer is boring.

Of course, competing with a tractor in strength or with a racing car in speed, who would be interested in that?

In any case, no matter how the AI is changed, players will learn to make it a "dumb computer".

If, however, the AI's intelligence is brought to the level of chess, it would certainly raise it as an opponent.

You contradict yourself ^ It's not a fact that it will be "dumb".

Also, it turned out that the computer's role is to be a spectator in a game with people. Therefore, I don't like the idea of making any changes to the gameplay.

That's just how it historically happened. And many have convinced themselves that it should be that way. But why?
If there were a real choice in practice, I wouldn't even discuss this issue.
Either wait for the opponent's turn, or rush in with a unit against a stronger one, even if it's not as skilled as a human player.

But firstly, this is a very complex and expensive process.

This is the key here. I just don't believe in the implementation of this idea. Although I would really like it.
It's like reaching for space travel; the game is really famous all over the world, and many companies like IBM tried to showcase their power in it. If a group of enthusiasts can improve the AI in Heroes, even as a fix, that would be a great achievement.

1. Should the AI have access to information about the attacking player's "key" spells? Resurrect, slow, haste, etc.

Ideally, no. But as an optional feature for those who like it, it could be left in.

2. Should the "secret" of using single units be left in? In this situation, the AI could distribute its 60 conditional centaurs not as 20/20/20, but as 1/54/1/1/1/1/1.

Of course, the AI should be aware of the method of using single units, removing the counter, and attacking with the main stack.

3. The AI could assess the player's SP, remaining mana, perform a kind of predictive analysis: "the player can cast slow one more time in 3 turns", go through the options of spells from the player's spellbook, and defend until the slow ends, if the damage from ranged stacks is insignificant and does not reduce the number of centaurs so much that the player's stack can kill them without significant losses, or the remaining centaurs can still reach and inflict some damage to the player's key stack.

That's a plus.
It would also be good to take into account that the AI, as soon as it gets its turn, immediately casts a spell, and then it is countered. For example, it gets its turn, casts slow, and in response, it gets haste. And so on.
That is, waiting and not casting immediately is also useful. But for this, it is necessary to correctly assess the situation on the battlefield.
And a spell like expert slow is a must-have, the AI should "know" that it should be there. And strive to get it. (And also think about how to counter it)

I see it this way, the AI should simulate a table of its possible actions and the player's actions for n+ turns until damage is dealt, and choose the combination that causes the greatest strategic damage, adjusting it each turn, depending on changes in the player's actions. The level of difficulty of the game will be determined by the depth of the n.

Good solution.

In general, are we talking about AI as a player, AI for neutral creatures, or AI as a battle simulator in general, one for all? As I understand it, it's for all?