A lot of the times this is an issue with the cleanliness of the litter box. Always make sure to keep it clean or else your kitty will refuse to use it. In this case though, that doesn't seem to be the issue since he's peeing in there. Like everyone else said, rule out any medical issues at the vet.
Most likely it's just an adjustment period since your kitty is still very young. Instead of that expensive air purifier, I would just get another litter box. Plenty of cats refuse to pee and poo in the same box, so this could be a quick fix.
Do you have another cat? Sometimes cats will poop outside the litter box if a 2nd cat is guarding it and being territorial. If this is the case, adding another litter box would solve this problem too.
Good luck!
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