You are correct that, under the IRA, the North American sourcing requirements don't apply to leases. However, the tax credit goes to the company leasing the vehicle to you. If they choose, they can then reduce the cost of the lease, thus remaining competitive while protecting their bottom line.
However, I don't see any indication on MINI USA's website that they are doing this. The estimated payment for leasing an SE is based on the MSRP just like an S, and the payment is about the same.
Obviously this is just a generic calculator, and things could be different when you attempt to strike a deal in person. The important point is that you realize that you don't get to claim a $7500 credit on your personal taxes.