> For example, one thing I always think about when cooking is how popular tomatoes and potatoes are in Indian cuisine (the former being essentially mandatory in most dishes), but since they were both brought over from the New World, the food from just 400 years ago would've been extremely different from what it is today.

Tomatoes in Italian cuisine are even more recent. While they were theoretically available from the 16th century, Europeans believed they were poisonous and refused to eat them. It was only around the mid-end of the 19th century that they became a popular and accepted part of the cuisine.