Most likely a blown head gasket. If you didn’t totally cook the engine when it overheated.
The head can be resurfaced and a thicker head gasket is available to keep the same clearances and compression. Remember….it’s just a Mini Cooper engine with stronger internal parts.
I’d get another opinion versus just a blanket quote of “ replace entire engine “.
Used low mileage i8 engines can be purchased for around $8-10k with a guarantee.
https://www.ebay.com/itm/37449944546...mis&media=COPY