Jeff, I play nursing/retirement homes sometime 2 or 3 times a week and the stage pass in my opinion is all you would ever need. Most facilities have two or three different levels of residents, independent, nursing and memory. For the independent groups I use a Fender Passport (stereo) and it is more than enough to fill the room. In all the places I play the performance area is no larger than 40’ x 60’ and maybe 40 people.
Now for the memory and nursing performances I use a small PA combo amp it’s an Alesis TransActive 50, which is of course mono. Unfortunately no longer made but it is the best small amp I have ever heard. Maybe just 20+ lbs.
These performances are very intimate with maybe 12 people max. They are truly “parlor” venues.
All of my files played from BIAB running on a MacBook Air. They are mixed in stereo and on the Passport I have the option of stereo or mono, it is an older model which has that capability.
So to help answer your question I don’t think it makes that much difference whether you use mono or stereo.
But you might consider 2 amps, one smaller so you can get in and out of a smaller nursing home performance and a PA for a party environment.