Before I describe the issue, I will mention that I don't actually need a solution; I just want to understand what's going on here.

So, given the following setup:
* AMD Ryzen 3500U, 8GB RAM (2GB assigned to integrated graphics), 250GB storage
* Wine version: 7.2 (using lutris, not fshack)
* Game: Solasta: Crown of the Magister

So, when I start the game with this WINE version, I get abysmal performance. In fact, there's so much lag in the main menu that it's essentially unusable. In other words, even setting the options, to try and reduce the graphic quality for better performance, is an ordeal. Furthermore, the game suddenly exits fairly quickly unless I add some extra swap space.

However, if I instead use Wine 7.2-fshack, the issues I mention disappear; the main menu runs smoothly without noticeable lag, and I've even been able to make a simple test dungeon with the dungeon maker and test it without any issues. (Hence why I don't actually need a solution to this issue.)

Any idea what's going on here?

This is just a shot in the dark (and may not have any relation to your promlem), but is the speed of your RAM the fastest that your motherboard supports ?...

As a wild guess, "fshack" in this case stands for "full screen hack" - it's a patch applied to wine which prevents the game taking control of your monitors. (Steams Proton also has this in place by default)

Effectively putting the game in a full screen window.

With that in mind, the full screen patch prevents the game from changing things like your monitors resolution or frequency. So it's possible that without the patch your game is setting the monitor to a bad frequency and/or resolution, which is causing the "lag".

Any chance the slower version is not using DXVK?

The WINE version (fshack versus not) is the only configuration difference between the two.