Switching careers - Is Masters In Finance / MBA My Only Hope?

Hi all and thanks for the time.

• I am 25, have a BSc in Computer Science, and have been a Software Dev at a Markets team at a BB IB.
• I want to try something new as nature of work because I am tired of pure coding (software dev) and I don't wanna do it for the rest of my career.
• I am also sure I do not want another technical vertical like cyber security, data science etc.
• I have been looking into strategy consulting, finance careers (IBD, Markets, Asset Mgmt, PE/HF) and product management in tech.
• I am not sure how to break into these - since I am in a quirky situation with my previous background plus I have missed the structured recruiting (post bachelor graduate schemes etc) -> not sure which roles/routes to target. Not even sure if those two will give me a chance due to my background.
• I tried recruiting for those but I get rejected because they all wanted someone with relevant exp. I think only PM in tech is the easiest due to the relationship between that and tech dev.
• I guess the biggest differentiator AFAIK is:

MiF -> If I want to focus on finance and easier grad schemes (as it essentially makes me a uni grad again)

MBA -> can get more senior roles especially given that I will have the necessary years of experience at the moment of application. Additionally, MBA seems better for consulting (associate recruiting) and tech PM, whilst giving me a chance IBD at associate?

Right now I am trying my luck with PM in Big Tech and front office semi-tech/finance Markets roles (as I am in Markets in some way right now).

I am in the UK, but open to relocate as well.

Thanks for the help.