Comparing MBA with non-business Masters

Hi all,
I am a 25yo, UK based, BSc Comp Sci, 3 software dev experience in a BB bank markets team.

My goal is to quit coding and move into strategy consulting or some thing more pure finance (like IBD). I am recruiting for (and almost sure I will get an offer for) a tech Product Manager role at another BB bank to make myself a bit more "commercial" (otherwise no one trusts you).

For all well known firms in what I mentioned recruiting is like this - grad schemes (too out of uni) and my experience (unless I get at least a year in that tech pm role) is a bit too detached for any experienced role (associate and above).

Whilst I continuously try applying, I may want to do a Masters to make my background more suitable. But due to current experience and wanting to optimise things I am a bit confused on what Masters I should choose - MBA, MiF/MiM, non-business type of Masters.

Logistically speaking, the benefit of an MBA it is more naturally inclined to my "timeline" and strategy consulting and IBD recruit in a structured fashion on the Associate level from different backgrounds.

On the other hand, MiF/MiM qualifies me for grad schemes (basically a clean reset?) where strat consulting entry level and IBD (if MiF) entry level will be easiest. This is assuming I will be ready to give away 4 years of experience at that point (but that is not too big of a concern as it is not that relevant).

The tricky part is, I have seen people with experience between their undergrad and masters (non-MBA) get associate/experienced roles. McKinsey even has it on their FAQ that if you have 4 or more years of experience between your undergrad and advanced degree (MBA, PhD or non-busines Masters) you qualify for associate.

By that logic does it matter whether you do a MBA or non-business masters? Surely that can't be the case because who would do an MBA then which is 2-3x the cost than your average Masters (even if it is in Finance or Management).

This is especially important for me to find out because I would actually love to do a MSc in a pure Life Science like Biochemistry (with a CS degree you can do that by contributing computationally and learning wet lab skills) so I can go and qualify for both digital and life science consulting (and healthcare team in IBD). Because I like life sciences.

A bit twisted but hopefully that makes sense.