Have I made a big mistake - rescue cat

[Bonden]

My boy cat died leaving my female as a solo cat.

Less than a week later I adopted a rescue boy, who is peeing on my clothes, bawling at night, the house stinks to high heaven, and I think I’ve made a stupid mistake in taking him.

He is desperate to see girl cat, he cries for her. She is curious. They “talk” through the door. My house has a door by the stairs so atm he has the run of upstairs, she downstairs.

But I can’t cope with the peeing in the house. He has a litter tray which he uses for poos. He’s timid with me, won’t come to me but will be in the room with me.

I woke at 5am because he’d peed by my bed and the stink of it woke me up.

I want to return him but feel so ashamed.

What did the rescue say about him? Did they say that he had any prior issues ? Was he fostered ? Had he experience of other cats?
It's hard to know with a rescue but ultimately the peeing is either a sign of a UTI or something like that or he is marking his territory.
I would contact the rescue and explain the situation and ask them for any suggestions. He's clearly not happy. I am not sure the curiosity is what you think it is

Rescue said he came from multicast house, would be suitable to live with a gentle cat (which she is), was shy but unaggressive (which he is).

She sits by the door and squeaks at him but runs away when I open the door a jar

Well it's possible he has a UTI
For the peeing you need to be meticulous about cleanjng and use an enzyme cleaner to get rid of smell. Is he peeing in the same place or just random?
If you think they are ok with each other you could try opening the doors and letting them see each other and explore more. I never bothered taking too long to introduce my cats but they are all old softies and are not that bothered about much.
It's really hard to know. Sorry OP. I wojld call the resuce though and explain the issues as it is possible there's some history there you dont know