As with everything in OSM, the answer is: there is not only one correct
way.
There is the one fraction which says that you should not add ways where there are none in reality. Then there is the other fraction that insists that routing only works properly if there is such an invisible way.
In practise, routers should be fine if you add the complete place to a route as long as you make sure that the outgoing ways are connected to the outline of the place. It might route you along the boundaries of the place which is still fine. Putting the place in the relation is certainly no error.
On the other hand, adding this additional way will also not hurt. So, just leave it as is. It's fine, too.
Personally, I tend to put places entirely into the relation. In parking lots, I generally add the ways where the cars can drive as highway=service and use those for the hiking route.
Thanks Sarah for your message. I have done ways throw places/parkings mainly for having a clean GPX file for the walkers.
I have contacted the FrancigenaLibrari to ask them if we can use the GPX files of the italian part on OSM. It's the official walk route. http://www.francigenalibrari.beniculturali.it/news1_en.html The idea is to use them to complete the relation but not adding ways. I have no answer yet.
Bonne journée Pierre-André