I haven't completely finished it, but I am close(I think)
First off, this was the kind of game I wanted to play at the moment, a (mostly) mindless incremental game, and it certainly scratched that itched. (plus it's a bonus I was able to play it on my potato PC, which many, no matter how simple, games in itch.io nowadays don't allow me to do)
Most of the criticism I have are less things you can "fix" in this game, but more like something to pay attention to for future games. And mind you, up until now, I still enjoyed it for what it is! These are mostly nitpicks(!!) thus don't take them too much to heart.
1. The UI is quite busy, too busy for what is essentially very basic concepts.
2. Some parts of the UI are frustrating to deal with, especially since there are timed bonuses here. Having to scroll back up in the right column to change the amount of upgrades you want to buy at once is annoying. Or scrolling down on the left column to see how many crowns you have just to quickly having to scroll up again to see a bonus you got and how much time you have left etc.
3. A basic of incremental games is that the more upgrades you buy, the less manual labor you have to do, however here constantly clicking remains the best and pretty much the only way to actually get credits. It pretty much forces the player to install an auto-clicker, especially with the timed bonuses. I know you made a joke in one of the achievements about carpal tunnel, but it's still a thing your game encourages, which is...not good. Incremental should eventually force players to strategize their scheduling, not force them to constantly click on a screen.
4. Sometimes a bonus appears that gives an insane amount of bonus for a short time, which pretty much....ruins half of the game. In the beginning it bypasses several levels at once. Late in the game it becomes more rare, but it becomes the only way to actually get some upgrades in a reasonable time, and thus having to wait hours for it appear and for you to be able to pay attention quick enough to make use of it is frustrating, and not in a fun way
5. There is an aspect to the prestige system that I haven't figured out what it wants me to do even after almost completing it, the actual skill tree. From what I understand it becomes active after 15 "checkmates", which is odd since you almost beat the game by that point. If there is another layer to the game after activating the skill tree, then you haven't made it clear that such a thing exist and...I don't like such a concept in the first place.
6. The random puzzles are a neat idea, especially since they give this chess-themed game some actual relevance to do with chess, but the bonus you get from completing them are almost never worth it. Plus it shows even more that the actual game has pretty much nothing to do with chess, despite looking like it should.