BallLM. A mod that changes and improves the original game balance.

Then I think it's better to leave the first tier with a one-time retaliatory strike. You could try applying it to units of tiers 1-4, which currently have a "killing blade."

My idea is that we need to completely remove the "single unit" tactic from the game, reduce the importance of the "focus fire" tactic, but not remove focus fire altogether – it's more interesting when it's still applicable in some specific cases. More tactics > fewer tactics.
In this regard, it would also be good to reduce speeds a la WGE – so that positioning makes the application of these tactics even more deliberate – even a unit without a retaliatory strike is dangerous to focus fire if it has good support.
Obviously, a one-time retaliatory strike, especially on units of tiers 1-4, which are mainly used as neutral guards, will again bring back the "single unit" tactic and thus will not solve the problem.

Improve the original balance, also by changing the mechanics that hinder the balance of power.

In my opinion, we need to break these tasks into two. Improving the mechanics is one thing. Balance is another. The first can be solved by introducing global mechanics, such as giving all units ability X, and the second is better to address separately for each faction, tier, and grade. Otherwise, one of the two will either fail to achieve balance, or the second task will interfere with the first and make the mechanics unappealing.
Although this statement is unsubstantiated, I really can't imagine how you can equalize everything with a global change and still leave interesting faction features.

I have an idea to give several units from each faction protection against archers (the "large shield" + "ally protection" abilities) and protection against mages ("magic resistance aura") or give all units 25% "magic immunity."

I would rather suggest, in the zero iteration, setting the skill of all spellcasters with combat spells to zero, the base damage of spells with zero skill to zero, and increasing the bonus to spell damage from magic. So that the lightning of two druids in one stack is not twice as weak as the lightning of two druids in different stacks – at least the problem with the stupid formula is solved.
But this will require careful balancing not only in terms of the damage of spellcasters, but also in terms of the damage of heroes, as it will also affect them.

Now, the enemy risks taking heavy losses when attacking if they try to overwhelm the enemy with numbers. A small army will now be able to inflict significant damage and will have a small chance of winning the battle.

So, now tricksters don't need to be warlocks? )

I think now, instead of this, I will increase the hit points of units by 2-3 times. Units will be slightly better protected from critical damage. Also, due to the "infinite retaliatory strike," you will have to withstand more damage than usual.

At first glance, after this, you will have to revise the stats of "glass cannons," which had the "deal a lot of damage and die" mechanic. Like the lizard riders.
Now they will no longer be able to one-shot an enemy stack, but, being surrounded, they will die even with increased health.
I would, in your place, first check if the introduction of a universal infinite retaliatory strike already reduces attacking tactics enough to change damage coefficients or increased health? That is, is there any point in these changes, or are they trying to fix something that has already been successfully fixed?

These are the points that remained untouched after applying global changes. It was assumed that global changes replace several smaller changes – the number of changes is significantly reduced and, therefore, it is easier to remember.

Well, if you conducted a detailed analysis for each faction, what was strengthened/weakened in it, ideally with numbers, and ideally with replays of battles; and it turned out that the balance really lacks some subtle changes – then I would agree ;)

Perhaps I will change the speeds of creatures instead of this change. What do you think about this option?
. 4-5 speed => 4 speed;
. 6-7 speed => 5 speed;
. more than 7 speed => 6 speed.

I think positively about reducing speeds, I'm afraid to say about the specific numbers. Perhaps there is nothing wrong with speeds of 3.