I'm not sure that there is a one size fits all answer for this one.
And, even in a digital forum, you're asking this question of a bunch of photographers.
Most, not all, bluetooth devices will occasionally give a "shout out" looking for "stuff" they are already paired to.
We have shared Mac wireless keyboards and touchpads in our classrooms, always on (in fact hard to turn off) and I just make it a habit to carry spare batteries. Then get replacements from IT when I have the time. I also take it on myself to change the batteries out at the beginning of every semester. My IT wants the dead batteries so I carry a small flashlight so I can properly discharge the batteries completely before I turn them in.