CFA level 1/2 breaking into IB as a Oxbridge non-Econ

Incoming Oxbridge Law student. Chose law because it genuinely interested me, but have been seriously considering IB for awhile now. I've been building DCF, LBO models and working through 400 questions for a feel of the technicals.

I've had a few conversations with people from the industry, but am looking for a more grounded picture:

1. For those who broke in from Oxbridge non-Econs degrees, were spring weeks/summer internships harder to land than Econs/STEM peers, or does the Oxbridge brand largely flatten during CV screening?

2. Do BB/EB recruiters actually distinguish between Oxbridge social sciences vs Econs/STEM?

3. Any advice for what a law student needs to do differently in years 1-2 beyond the obvious internships etc.

Not looking for reassurance, and appreciate the frank assessment. Thanks in advance