Sponsorship options depend more on the target office, role and your work authorization than on whether you hold a Master's.

MBB and other consulting firms can have different policies by country and recruiting cycle. An office that sponsors one category of hire may not sponsor another, and eligibility is not guaranteed by a degree.

A graduate seeking a UK role may face a different process than someone seeking a US role, even with the same degree. The office's recruiting team is the right source for the current rule.

Shortlist offices where you are willing and eligible to work. Ask recruiters whether the office considers international non-MBA Master’s applicants and can support your particular visa route. Use the guidance on recruiting as an international Master’s student to frame those questions.

A friend got a different visa answer from the same firm's UK and US recruiters. Office really matters.

Any advice on when to raise sponsorship with recruiters?

Anyone recruiting in Canada? I keep finding advice that's only about the US.

The job listing sometimes says nothing about sponsorship.

I'd check this before spending weeks on casing, ngl.