I agree, “ancient” is a loaded term. It is very much used by white people to justify shoving something in a museum instead of letting Indigenous people keep it. “Oh, but it’s ancient, so clearly we need to take this sacred object and keep it. For posterity.” We do it with Africa, with the Americas, with South and Southeast Asia. Basically anywhere there was a local population we wanted to dominate, white academics took their stuff and shoved it in a museum and acted like the people it came from were all gone already.
“Pre-colonial” is obviously the most accurate term for old things from before Europeans arrived. Although I am kinda partial to “vintage.” Calling an item or a place “vintage Aztec” seems, to me at least, to ascribe continuing value and richness to it to modern people where “ancient” implies a separation from anything modern. “Vintage” feels like a gift from older people to now for the next generation to enjoy, where “ancient” feels like it was lost or abandoned and found by accident.