Heroes 5.5 WarGame Edition - Tactical Edition.

As an alternative, by the way, you can increase mana, like with the Avatar of Death for Arantir... That is, you either summon a small phoenix and continue casting spells, or you summon a super-powerful creature once and spend the rest of the battle as a weakling. Of course, this is less original...

There is no such technical possibility.
As mentioned above, the phoenix will never be a super-powerful creature, i.e., it won't single-handedly decimate an army. Rather, it acts as a regular tier 7 unit, sometimes twice as strong with high magic power.

Arantir, by the way, is one of the playable heroes in the mod, so his ability to fully absorb mana is relevant. How the avatar will grow for Arantir is still being considered, but it will likely only increase attack and defense stats, unlike the phoenix. That is, not in size, but in ability. Initially, I considered this mechanic specifically for the phoenix, but rejected it due to the excessively rapid increase in power with high magic power, while it is suitable for the Avatar, since its level is limited much more strictly than magic power.

Most likely, the Avatar will look something like this:
Cost = Hero Level
Initiative = Hero Level (it is necessary to use initiative to justify the ridiculously low cost at low levels)
Attack = 20 + Hero Level
Defense = 20 + Hero Level
All other stats and abilities are fixed and do not depend on the hero level.

Added 33 minutes ago

The idea is good, I like it. But in my humble opinion, the dependence of initiative on magic power is too great... The ideal phoenix will have an initiative of around 4-6, which is a very useful parameter for a summon; the more it interferes with the enemy, the better. With an initiative of 6, this creature is useless in my humble opinion...

But how can it be at 4-6 if damage and HP grow quickly, and initiative only starts to decrease rapidly below 6 (by 10% per spell power).

The peak form, as I already said, comes with magic power = 17.
A phoenix with initiative 6, damage 120, and HP 510 will be much stronger than a phoenix with initiative 13, damage 48, and HP 150.
Also, consider the fire shield that returns 100% of the damage; a larger phoenix will leave much more burns behind than a smaller one.

The peak of active form, in terms of maximum damage per unit of time, occurs at magic power 12 - this is a phoenix with initiative 9, damage 90, and HP 360. As you can see, at magic power = 17, it decreases in "activity" by only 10%, but is 40% stronger.
Keep in mind that stats play twice as much of a role, i.e., magic power = 12 in Warlords of the Ancient Races (WOTAR) is approximately equivalent to 24 in the original, and 17 is 34. Because physical stats give twice the bonus (10% instead of 5%), and the mage won't have time to increase magical stats to astronomical levels. This is not a game about "killing everyone, leveling up to 30+, running around the map for bonuses, and dressing in relics from head to toe." What will happen under these conditions in terms of balance is completely irrelevant, since they have a very distant relationship to strategy.

Below 10 (or at least 9), it's unusable. It will simply be ignored. Unless with magic power 60, it can one-shot someone once with initiative 1 and then summon a new one.

This phoenix is designed not for the original game, but for WOTAR. This means that the summoned creature will have time to be useful even with low initiative, because there is no such thing here that half the army will be destroyed on the first turn.

It makes sense that as the size and power increase, the creature should become more cumbersome. But is this applicable to the phoenix, for which you have to spend a lot of mana on a powerful spell, and get either a weakling with high initiative or a fat guy who moves once every 10 normal turns?...I don't know.

You don't need a cumbersome phoenix - just don't use it with magic power above 17, what's the problem. Instead of a phoenix for 20 mana, there are alternative elementals for 18, which can be easily obtained during leveling or from a ring. There, the spell power is 20+, if the opponent allows you to level up that much, and it will be useful.

As I already said, the phoenix has become similar to short-term buffs. Of course, the duration = 0.25*(Magic Power+1) strongly depends on magic power, but at the same time, with magic power above 20, you get more than 5 rounds, which is usually unnecessary, and it is better to use super magic on other spells. In general, it can be said that in a large battle, the phoenix on the field is not a warrior. You are asking for too much from one small bird.