Congratulations on the offer! In terms of your question:
Q: I have just accepted an MBB full-time offer in the SEA region which will commence in 2023 (flexible and can be deferred to 2024). May I know if it's legal to accept a different MBB firm's internship offer in another location (think NY, SF, London etc) prior to my full-time start date?
Unless there is something in the contract covering this case, it is not a problem to do internships before your full-time role starts if you then join the firm that extended the full-time offer - there is no direct contrast between the two options (although, the second firm may extend a full-time offer as well).
If instead you don’t join the first firm after you signed, the consequences depend on the local legislation and contract. I know a candidate who had a financial penalty in the contract in case he didn’t join a Tier 2 in China after signing.