No actual technical solution here, but it smells slightly of XY-Problems.
From what you described it seems the main issues are
too many calls
not knowing who's calling
not wanting to answer the phone
not reaching the phone in time
Maybe you could look into solutions like setting a custom ringtone for important callers or having the phone announce caller names so your mother can decide if she wants to make the effort to get her phone.
I'm speculating a bit here but I can imagine that getting up and answering the phone is exhausting for your mother. Also if her mindset is " a ringing phone means it's important" that could make it even more stressful.
Maybe you could find a way to let her silence all calls except caregivers and ICE contacts. (On Android DND exceptions could work for that)
That way she doesn't feel pressured to answer the phone every time it rings and stays reachable.
If it's actually just the physical issue of reaching the phone in time, does she have a convenient way to carry the phone indoors like a lanyard?