Help: My cat started peeing outside of litter box!

Hi everyone, in this post I am asking for advice.

I have a 5 year old male cat. I let me cat both inside and outside of the home.

Recently, my girlfriend moved in with me and brought her cat. This cat is a female that only sometimes goes outside.

My male cat does not care about the female cat, no hissing, no violence, just goes about his business. However, the female cat very much does not like the male cat. The female hisses, yells, and is afraid of the male cat.

So recently, my male cat has started marking his territory on door corners and on grocery bags and boxes but spraying urine. I have tried scolding, putting him in timeout, and most recently we put both cats in a closet together overnight.

Any suggestions? Is there anything else I can do?

Thank you!