I'm generally not a huge fan of this sort of dice rolling puzzle game, and the GMTK jam hasn't been great therapy for it. That being said, while this game does have some of the same problems, there are also a few things it does pretty well.
First, why do I generally dislike this genre? It mostly comes down to finding it easier to solve puzzles by accident than by reasonig about the level. The best puzzles are those that require you to have key insights about them in order to be able to solve them, which often includes backward reasoning, where you need to figure out what the solved state looks like and work your way backwards from there.
A good example of backwards reasoing is the very last level, where I managed to work out two "winning states" and then could work my way forward to reach one of them. I was a bit frustrated with the level at times, especially since for most of it I hadn't figured out how to use the example die yet, but in the end, the solution felt very satisfying.
Speaking of the example die, it's a great feature, especially for backwards reasoning purposes, but please document somewhere how to use it! As I mentioned, I hadn't even realised I could use it until the very last stage. Also, I would probably swap the functionality of QE and AD so that WASD matches the behaviour of the arrow keys.
Another thing your game mostly does well is that even in forwards-reasoning puzzles, the possibility tree is pretty limited so you can sort of do a "breadth-first-seach" here. Also, figuring out losing states (e.g. a 4 being bad until the parity lines up perfectly) was an enjoyable process. Notable good example: Hard3. Notable examples where I found the possibility tree to branch out of conrol: Hard5 and Hard6.
Usually it's a good idea to have an undo system in your puzzle game unless you have a really good reason not to. I guess you could argue that this forces the player to explore the forward tree more deliberately, but I'm not sure that's enough reason to deny the player what is essentially a convenience feature.
Music is well composed, but the instruments feel a little too synthetic for my taste and you should probably also add some dynamics and stuff, but most importantly, you probably want to add at least one more track. Hearing the same thing over and over again eventually gets repetitive, no matter how good the music is.
All in all, one of the better dice rolling games I think came out of the jam and you seem to be a very capable puzzle designer. If you can figure out a way to make more "lynchpin" puzzles (where you need an "a-ha!" moment to solve them), that would be great! I think the genre unfortunately just has its limitations, but I'll be glad to be proven wrong.