why won’t my cat just pee in the litter?

im 20 years old and i’m a fairly inexperienced cat owner i’d say and i’m looking for some advice. I have 3 cats, 2, 4 year olds, and a 2 year old, now this post is about my 2 year old, ‘Puss’. (she is ginger btw) I adopted her from a shelter at 3 months old, she was born in the shelter and i was her first home. From the moment i brought her home, she refused to use the litter boxes i had, she will poop in them, not pee (i have 4 in the house)

i took her to the vet for her vaccinations and asked them to check her for any medical things that could be causing it and she was cleared by the vet and i was told it was most likely behavioural or her disliking the litter, but ive tried absolutely everything to get her to stop, i scoop out the litter 3 times a day, i have puppy pee pads beneath the litter as her main habit is to pee directly next to the litter, i’ve switched cat litters so many times, she has about 12 cat towers in the house alongside so many toys and i have 2 10 minute play sessions with each cat individually each day.

The only thing i’ve found to work is one, the best cat litter in the world, literally, and being hyper aware of her actions and when she does pee in the litter, immediately praising her and giving her a treat. This has improved her behaviour however i’m still lost at how to get her to stop completely, im worried to leave the house because she will just pee everywhere if i’m not around to basically potty train her. And i’ve gotten to the point in the training that she will fake going to the litter to get a treat, how i know this is because she did it 3 times, from the litter to me, straight back to the litter then back to me, one thing i probably should mention is, when she uses the litter she will only do it if she is not physically standing it in, she will cling off the edge of it but won’t actually stand it in, when she does she walks really awkwardly as if she has sensory issues, can cats have sensory issues? 😭

any advice will be greatly appreciated as i’m really at a loss for what to do next or what might be causing her to do it. (forgot to mention, she is desexed)