"Baggage" describes what it is. "Luggage" describes what is done with it.

The phrase "they come with some baggage" is used about the unprocessed stuff that we have. "They come with some luggage" is not.

Baggage is a noun — it is about the bundles and bags of things.
Luggage is a verb — it is what you "lug" about.

It gives me hope that we respect when people are doing something about their stuff.