Hi there
I completely empathize with you on this one, I'm an international student too and work part-time. The good news is, I've found lots of support available at Durham to help us with this. When I started back in 2021, the weekly hours cap was 12 but now it's been changed to 15 (it's mentioned on
this website). However, this restriction only applies when all your employment is with the university and wouldn't really be an issue if you're working for an external employer. I'm currently doing 2 jobs, both within the uni, and they hours add up to 13. I also secured an offer for a third job within the uni again but it was retracted because of the cap on hours. This is only because they don't want the students to be focusing too much on working and keep their studies as their primary target.
On the support side of things, there are part-time jobs exclusive for Durham students which are super flexible, within uni departments, many of them involve online work so you don't have to be in a physical office and involve less competition because they're only for Durham students. I secured both my jobs through this and I'm loving my experience. These vacancies, as well as external ones, are advertised on the
Student Services Portal which you can access once you are formally enrolled with the uni. The Careers & Enterprise centre has loads of resources to help you in the application process, ranging from drafting CVs and cover letters to mock interviews and assessment centres. You can also book 1-1 appointments with a careers advisor to help you in your search and plan your career journey. Also some very amazing events are run by C&E including part-time jobs and volunteering fair where employers advertising vacancies come on campus and you can interact with them (and possibly share your CV for review). These are usually held in Michaelmas term.
Hope that helps and let me know if you have more questions

-Himieka