Target to Non-Target...Am I F***ed?!

Hey guys! I am a student studying in a non-target (Exeter uni) doing a non-finance subject, going onto second year. Prior to this I was in a target uni doing STEM but I decided to switch to the UK. Had internship experience in a small M&A firm, a big 4 and levfin in a big bank. However due to a lot of personal reasons I did not apply for any internships for this year 2023 summer. 

So now, I got this list of disadvantages:

1. Non target 

2. Non finance subject 

3. One year employment gap

I'd love to try my hand again in finance but I just want to know a few things:

1. What divisions would be easier for me to break into?

2. Should I still include my old university in my resume?

3. How should I plan my career in general as someone with so many disadvantages?