RNG can be hard sometimes. The dissatisfaction is tied in with knowing even if you did better as a player it wouldn't matter because RNG has cheated you. I liked that you had planned to use it as a narrative point, it would be a powerful reflection of reality where you can do nothing wrong and still lose. That narrative would also temper the expectation of the player since they are going at it from an experience rather than a game of skill
Personally my belief (and mind you this is a challenge to implement sometimes) is to structure RNG so that it can make a challenge more difficult to complete, but never absolutely impossible. That gives the player a feel of agency and the sense that by getting better they can improve. The golden rule I try to follow is to try to never leave the player feeling like they have been cheated by the game
I played quite a few rounds of your game and I felt the difficulty was well balanced, I only completely lost all my cats a few times, but having played it for a bit I realized I hit a wall in terms of being able to get better at my strategy because RNG would ultimately decide if it was possible to get a perfect game or not, and most of the time it would not.
All that being said I did rate your game very highly because everything else was basically perfect. It is a really fun game with a silly theme as you scramble to save the cats. It felt decently balanced and I had a lot of fun. Dont take the RNG feedback too critically because you really made an awesome game!