I got very excited when you posted this game on the Dominion subreddit. This felt more like a blend of Dominion and Slay the Spire than Balatro. Regardless, you did an incredible job with this game, I love it. I spent the entire morning playing and finally was able to finish a run. I didn't track how many runs it took to complete one but it was probably around 15. The run that I won was very satisfying. I was able to draw my entire deck pretty consistently and even gain and play stuff once I had an empty deck and discard. Still need work to find the correct amount of specific cards to have in my deck.
As far as difficulty goes I think it's great to start. The cards themselves are surprisingly well balanced. Some obviously stronger than others, the cards that allow you to convert your gold into card draw or mana were very strong but I don't think I could have won without them. You still have to manage and strike the right amount of card draw vs manna generation and obviously you have plenty of shuffle luck as well. And the card draft concept is genius. The easiest way to introduce a sliding difficulty would probably be amount of turns in each new level, amount of turns to carry over or increased number of shields to break per round but I didn't have any nerfs or buffs for specific cards in mind. Will come back if anything comes up as I continue playing.
As far as previous comments go, I am on the fence as far as deck visibility. I think knowing the contents of your deck and what you have bought/trashed are part of what makes Dominion difficult. I do think it would be beneficial to have deck visibility and stats after losing or winning a run to keep that knowledge for future games but as far as in-game I think you would want to only allow that at certain times. I also didn't have a problem with the turn counter. I can understand the other player's point but I would be fine with it either way.
My biggest recommendation for improvement would be a back button. Obviously you shouldn't be able to go back if you've revealed new information through card draw or deck spying but mis-clicks cost me big a few times (let me know if I am missing this somewhere I couldn't seem to find anything). Also, a card concept I was wishing I had while playing was something that would give start of turn draw the next hand similar to duration cards in Dominion.
Thanks again for sharing this!