Cat refuses to use litter-box to pee PLZ HELP

To give Y'all as much info as possible:

My GF and I adopted a cat who had been in the shelter for nearly a year and was 3 years old. She is an absolute sweetheart so about a year after that we adopted a second cat the day it was supposed to be put down by the shelter. We separated the 2 cats into 2 sections of the apartment for about 4-5 days with their own litter box so they could get used to each other through a door. The new cat peed on the bathmat and some towels we had in the bathroom but we thought it was probably just an accident. We then swapped rooms so they could get used to each others scent however the new cat jumped on our bed and let loose all her pee right in the middle of the bed..... We cleaned it up and closed that door but about a day later we found pee on a couch cushion. So we swapped the rooms again putting her back in the bathroom and letting our first cat roam the rest of the apartment. Eventually we decided it was time to let both cats have free reign of the apartment. However the chronic peeing got worse. She has peed on Clothes, Clothes that are in the dryer, every couch cushion, the bathmat(like 100 times), My backpack, My gym back, countless numbers of shoes, throw pillows, blankets, you name it she has peed on it. She has even peed IN HER OWN BED and then slept in it..... We aren't talking like a little pee to mark we are talking about huge bladder fulls. So we tried changing the type of litter and that didn't work so we re-separated the cats. But now even separating them doesn't stop it. She is in a bathroom with a cat tree (For some reason she doesn't pee on the cat tree) and there is no towels, clothes, carpet, nothing to absorb her pee but the cat box. So here are the tricky ways she has peed in there. She has reached under the door and pulled clothes under the door to pee on. She has peed on cloth toys that she has in there when she cant do that she just pees on the tile floor (That is her last resort). Well now she has discovered the air filter on the top of the litter box and she has jumped up there and peed on top of her litter box on the air filter twice. This has been going on for about a year and a half now and only seems to be getting worse. If anyone has any suggestions on things we can try.

So here are some things we tried and have not worked:
We have changed the litter multiple times.
We talked to our vet and she ran a pee test to see if there was anything medical and has found nothing.
We have tried a calming cat diffuser.
We have tried anxiety treats.
We Spoke with our vet again and she suggested using a type of anxiety medication but so far it has been 2 week and we have not noticed any difference.

This is very tricky & I hope someone will come along & help you. We once had a female spayed cat who peed everywhere. She just could not stop. She was basically an outside cat, but was allowed in our basement. I am told that inappropriate peeing is the #1 reason cats are abandoned.

S shadow767
I'm bumping this post up so more members will see it.

Have you tried LOTS of litter boxes and different types of litter? Does she have control of her bladder when she sleeps? Is she spayed? What does your vet say? Also you may not like them long term, but pee pads might be a short term solution. If she is feeling nervous a litter box without a top part might make her feel more secure. I had a cat that peed everywhere (due to an injury.) I can offer you this helpful tip, Baking Soda. Buy lots of it If you add about half a box to a load of pee soaked laundry (or a whole small box if you want to over do it) then wash your clothes like normal it WILL remove the pee smell. Which should save some of your clothes

To answer your questions for others who may run into this problem.

-She is spayed.
-She has no problem controlling her bladder when she sleeps (considering we haven't found pee in any places she loves to sleep)
-Our vet says she probably just has anxiety.
-Also we have been using Natures Miracle urine cleaning spray to clean with and it has worked great.

Now onto THE SOLUTION!!!!!

We took our cats with us to visit family where we bought a cheap litter box with no top just to make due while we visited. Our family members have 3 house cats of their own and during those 4 days there was no accidents! So we brought that box home to test it and so far its been 1 week without finding any pee anywhere. @DantesHuman you were spot on!

We have guessed that she doesn't feel safe going into a litter box with a top and she feels like she might get trapped.

I will send an Update in a month or so if this really does continue to work. I think the next step is to leave our bathmat on the ground and see if she still uses the box.

Update there was 1 weekend we had left for a trip that our cat peed on a bunch of stuff. But since then we have had 2 other trips and no pee anywhere! Looks like all it took was an uncovered litter box.

My cat peed outside the box, but very close to it. By peeing as close to the litter box as possible, I figured that she knew she needed to pee in the box but just didn't feel she could. So I tried several different kinds of litter but it didn't seem to matter. Eventually I discovered that it was not the kind of litter I used, but the depth of it. I was filling the box with 4" of litter per the package recommendation. Once I removed half the litter she consistently used her litter box and hasn't peed outside the litter box in a year and a half.