well.... it's a bit unsettling to read about witchers and other subtleties—I personally knew nothing about this in principle

There is a good table on the Gugolok website showing which hero class is obtained when two primary skills currently held by the hero intersect. It also describes what additional benefits a hero of that class receives. For example, you have no poison magic, no poison bubbles, and no poisoning artifacts. But you desperately need poison for this particular Walkthrough. We level up the hero in a certain way and get a class—Assassin (or something like that). A hero of such a class gains the ability to poison an army upon striking or shooting (I think that's the case too). Poison will be applied to them as if you had cast poison magic, even though you don't have it :) This can be very useful sometimes.

... then I found out about "offloading"... but I just couldn't get past the left neutrals in the center using offloading (the right ones either). It seems there is some trick to it. I'd like to read how it was done ...

It is impossible to get past the right neutrals in the center by offloading. But the left ones can be bypassed. For this, you needed to take a couple of units with you. You can pick up Efreeti from the dwelling there, + offload an Efreeti and buy a bunch of Imps. When you are standing right next to the hero, you first offload one unit, then a second, and ONLY THEN do you offload the main army and the hero with the tombs. At this moment, he cannot jump to where the two previously offloaded units are standing, because those spaces are occupied ;) And then he makes a jump behind that neutral. Well, then you jump a couple more times and you've broken through without a fight.

... or watch a video (recorded with Camtasia, for example).

Why bother with a video for some reason—I don't know how to do that. Just download the saves. I've uploaded two saves for the end of the 1st and 2nd turn. See the links in the thread above. In the games, there is a turn review mode that shows what the player did; in the review mode, there is a pause (spacebar), and while paused, you can poke around and look into the hero's army window and pockets—see what's going on there. I've already written about this.

my hero just shifts to the right and cannot get behind the neutrals. at the bottom—it's easy. by the way, it's unclear why all these perturbations are needed if the center can be passed without a fight? get grand stealth and go forward.

Grand stealth cannot pass everywhere; the passage doesn't allow it—it's narrow and there is a neutral standing there. But stealth allows you to get right up to them, and sometimes this can be done even without stealth—mapmaker glitches or tricks with a tomb thrown at your own feet in front of that neutral. Then you can add units to the hero if the hero cannot jump by offloading himself—as you described. Then you scatter units first so they occupy the suspected spots where your hero is aiming, then you jump with the hero, and since the spaces are occupied, he climbs over the neutral. This does NOT ALWAYS and NOT EVERYWHERE work. You need to find where you can squeeze through and where you can't. For example, the right neutral in the center cannot be passed at all, not even by a grand stealth hero.

by the way, it's unclear why all these perturbations are needed if the center can be passed without a fight? get grand stealth and go forward.

Well, on the other side, you also have to fight the castle guards. Therefore, leveling up the fighters is not extra, if only so you don't have to chew through this guard with fairies for a long time. And castles, money, minerals—that's more additional troops, artifacts—this is needed for points at the end of the game—because the secondary criterion for determining the winner in case of equal days is the points scored in this tournament, and the third parameter is oil.
So, on the third day, we grab the nearest neutral Fortress on the other side. Moreover, I couldn't break the ballistas with the stealth hero, but by removing one guard squad at the gates, I managed to push the tombs into the Fortress and they came to life. From there, powerful fire-witchers emerged and beat the ballistas, completely clearing the area in front of the gates. Then two went (the stealth hero's turn was already over, but the revived heroes had a full turn) to another neutral Fortress where the guard was Cyclopes + Harpies in pairs in one squad. I didn't have time to figure out how to take them out on that territory, there were also "booholders" in the quest towers, but I knew the tactics of two fire-fighters. One constantly cast forgetfulness on the Cyclopes. The second poured flamethrowers on the Harpies. Witchcraft doesn't work on Harpies because the retaliation doesn't trigger—Harpies are not retaliated against. When the Harpies burn up, the first continues to hold the Cyclopes with magic—they constantly skip their turn. The second fire-fighter begins roasting the Cyclopes :) Such a fight takes very little real time, but a lot of mana :) Then in one neutral settlement, a zero-level hero is bought (this is necessary to get maximum points from the last battle—because a high-level hero will be given fewer points for the last fight). But it would be very difficult for a zero-level hero to defeat the enemy in the last Fortress. But since we worked hard on previous turns and gathered ALL SORTS of junk, we put a bunch of artifacts on him, give him many different bottles, and he's already doing quite well—no joke :) That's basically why all the perturbations are needed in the very first turns. Because it's unknown what awaits us in the subsequent turns ;)