I don't agree with that dictionary entry at all. We also say 'luggage' in AE, if the question is just what you call the stuff you put in the trunk of your car on a trip, or the stuff you check on an airplane. A porter at a hotel, for example, would say, Do you have any luggage? or Can I help you with your luggage?, not baggage.
My impression is that 'baggage' in this sense survives mainly in fixed phrases such as on signs and in two-word phrases: baggage handler, baggage claim area, etc. But as the second word it can often go either way: checked luggage/baggage, carry-on luggage/baggage. I probably wouldn't say hand baggage, though, only hand luggage.
As a word standing alone, I think 'baggage' nowadays is usually figurative: emotional baggage, psychological baggage, baggage from a previous relationship.