I let you fight that one out with your inspector. Sure if your washer dryer is in your den is it a laundry area or a den? My bet is that a 240 dryer is going to need gfci in most instances.
Do you really need a definition for a laundry area. If you use the words to launder then it would only apply to the washer.
I can be on board with the words "to launder" like you mentioned and only the washer makes it a laundry area.
If you have both washer and dryer in the den, you still have a laundry area it just happens to also be within the den IMO.
"Mud rooms" with laundry and bath were once fairly common thing around here, especially in farmhouses. You come in have a place to take off your dirty clothes, laundry is right there, plus you can shower in same room before entering the rest of the house. IMO any requirement that applies to laundry or bath also applies to such rooms. When such rooms were real common we didn't have many the current requirements. The 1500 VA laundry circuit was a requirement and GFCI for bath receptacles was a requirement, AFCI didn't exist yet. Today I would think an inspector would like to see one circuit to supply the laundry, one circuit to supply the bath receptacles, would be somewhat flexible on what other outlets in same room might be allowed on either of those circuits, and would require all receptacles to have GFCI protection and if 2020 NEC applies then that would include a 30 amp 120/240 dryer receptacle as well.