If you have gotten a cat from battles, such as Persian, bred, old man Marvin, or Scottish fold, cats cannot be bought anymore(ONLY ON WEB VER, MOBILE VERSION IS WORKING), I've had this same glitch, it's perfectly okay as the cat shop isn't the best (no offense to creator) the cats you get from battles are somewhat better when leveled up than the 1-star starters. :)
^^^ !!!!! additionally this game has been around since 2018 AND is a hackathon project (as said in the github) so i doubt game creator would really update the game as she has other priorities. luckily once you get through, you have many opportunities to get powerful cats, such as caticorn and robocat, both 4 star cats (with max damages of 63 and 85 respectively.)