I'm having a specific problem in this mission. On the first day, I move the heroes, their turns end, and I skip a day... and skipping a day takes about 5 minutes. Although it could take a maximum of a minute and a half. Please, comrades, tell me what to do. I'm starting to feel like cheating, but I don't want to because I'll miss a cool cutscene, and I like the cutscenes! Help me. Thank you in advance.
P.S. The game version is 1.1. I've heard it's buggy, but in some places.

Well, from the very beginning, the AI also took a long time to think (compared to other missions, it was clearly noticeable), not five minutes, of course, but it could think for a minute (especially, I think, the brown one took a long time), but there's nothing you can do about it; at the beginning, it has eight castles. Then, as the territory is gradually captured, the situation slowly improves. Version 1.1 really has a lot of bugs, so I advise you to patch to a more serious version, preferably to version 1.5. But I don't think this will significantly affect the problem. Most likely, you just don't have enough RAM :)