How to get job in UK from India

So… my fiancee is in the UK for her job and apparently I am in a long distance relationship with both her and her education loan (she needs ~3 years more to clear it).

Meanwhile, I have 0 clue how to move myself closer to the UK part of this equation.

I am a frontend developer at a startup in bangalore with 5 yoe. I am leading all Frontend initiatives at my current company.

I am upskilling right now and open to picking up niche/specialized skills that actually make my resume stand out.

Couple of questions:

Haven't touched LeetCode seriously. Is it one of those "do it or perish" kind of things?

My resume has no shiny FAANG logos, just startup chaos (I love startups). Should I aim for a big MNC just for the brand tag?

I contribute to open source (mostly JS, occasionally). Should I double down and be more consistent there?

And the eternal mystery: how do you even reach recruiters?

Any advice would be helpful 🙏