The problem, of course, is the same as for most people here: capturing the first 2 castles in the basement and then hitting a dead end. Because they keep coming from 2 sides the moment you step away. And letting them take the capital would be too costly, since you lose the capitol.

You shouldn't hold them at all. On 1-2-1 buy up troops and run to the castle next to the Dragon Utopia in the northwest. And it is preferable to take the Dragon Utopia before the opponent. As for the money? To hell with it, they'll give you some in the Dragon Utopia.

by the way, a question - on Veteran and Hero difficulty, have you experienced this: as soon as the mission starts and we approach the castle (the very first one), a Warlock (any) arrives there with an army larger than that of ГГ? This happens to me constantly, and I can't even take the first city, even though Railag is pumped up to 40 - simply a lack of meat...

Generally, he usually just stands near the city. And on the enemy's first turn, he charges at Railag or Shadia, whoever is closer.
If, for example, Railag has upgraded logistics, then Railag can reach him on his own turn. You can put out a single minotaur for the fight and stifle the enemy, who likes to bunch up, with Meteor Storms. Of course, it is highly desirable to have developed Sorcery, Chain Lightning, and all Chaos magic.
If Shadia has Expert Logistics, she can not only reach the enemy but also enter the city, as she initially stands closer to the city than Railag.
Both of mine had logistics. Therefore, I hit the adversary with Railag (he is stronger), and entered the city with Shadia.
But even if there are no logistics, you don't need to take the city. The enemy will attack on their own.
On the second turn, another enemy usually arrives. The main thing here is that he attacks the castle rather than chasing after one of the heroes. But he might not arrive; in that case, it's better to replay and make sure he does. The fewer powerful heroes the enemy has, the better.

P.S. What do you mean Railag is pumped up to 40?