Lots of useful ideas here.
I fear I may have given a rather false impression of my neighbour. She is elderly and very deaf but otherwise is very active. She lives alone and has no carers etc., she gardens, she lip reads very well, she drives, she uses a tablet more, and more expertly, than I do, she gambles when playing bridge and ( in normal times) she sings in a choir and has a very active social life. I think it is perhaps because of this social life that she is so reluctant to have anything that might make her appear to be disabled.
She does though seem to want a solution to the doorbell issue, though she does not seem so focused on the smoke alarm.
I will list all the ideas that you have all suggested and let her and her 2 adult children ( who live elsewhere) decide what she will do to enable her to answer her "doorbell."
Many thanks to all who contributed.
Rod