Hi Habi,
I've added a couple of other buildings with this tag recently.

I'm not convinced that amenity=sheltered_housing is more suited to those type of building than the building key, but please try to convince me!

My thoughts: none of them have been accepted as a key or value. The only page that I could find is an abandoned proposal for amenity=sheltered_housing.
Looking at taginfo, building or residential = sheltered_housing seems slightly more popular (I added no more than 10 building with this tag myself).
In my opinion, it's very similar to building=dormitory (which is a de facto tag as well, but at least documented on the wiki). From what I understood, those are “normal” buildings but adapted for seniors or people with disabilities.

What do you think? Did I miss something?