I like the idea of more sudoku games that play around with theme and variant rules.
There are a few QoL elements that are missing that are present in vanilla and variant sudoku software (I'm referring to Sudokupad and the like more so than games) like notes (even as simple as 9 distinct colors that can be placed in the background of each tile at will) or highlighting all copies of the monster you have selected or on double click. However, I like that you have multiple control modes allowing for new players to use whatever feels natural to them.
For the poison trap, I was able to figure out what went in the poisoned spot and wait to place it until the end. It didn't change too much, but I'm not sure how much it should change.
In sudoku, I tend to like explicit rules with unclear consequences, so I would like more clarity in the items and trap effects. However, if done well in the full game, it could be a unique draw for this game. Sudoku for sudoku players has become quite refined, so including hardcore sudoku solvers in the target audience might not be wise (you can take all of my suggestions with a grain of salt).
It is an interesting decision to have multiple solutions for some puzzles. I had a few puzzles down to what they call a "deadly pattern" in sudoku, as in the image below.
After this point, I would enter in the last options and never lost HP. Either both solutions are accepted or I got lucky with 1/16 odds (4 puzzles with a 50/50).
I found this game through Indie Game Clinic on YouTube.