The more common thing (now) is to make the new work high-quality but clearly distinct. I presume that's what's planned here -- don't build all the basement wall

The more common thing (now) is to make the new work high-quality but clearly distinct. I presume that's what's planned here -- don't build all the basement walls up again with similar stone to an original-style stage floor, instead add a steel structure over all the old stuff holding a modern floor, with glass skylights for touring the ruins below.