What happens to POA for the other person if that POA becomes incapable?

You need to speak to Granny's Sister or members of her immediate family. If she is not suffering from dementia she will have to create another POA for herself. I am surprised she is not aware of the descent into dementia of the sister she has been dependent on, if she is mentally capable.
Meanwhile, all mail you are receiving, should be returned by you, as POA for your Grandmother, to the sender with a letter (print lots of them) explaining you are POA for your Grandmother, and that she is incapable as fulfilling any duties of POA for anyone now and in future. This will lead the entities to contact the sister. If this sister is currently herself already demented (My guess as your Granny was already acting for her, apparently) then the family will have to intervene to get guardianship, which will negate any former POAs she may have done.
If there IS no family for Granny's sister (my guess, as she made her sister POA) then there is a larger problem if this sister already suffers from dementia or is in care. This would be a problem to take to an elder law attorney or Adult Protective so that they can arrange State guardianship and appointment of a fiduciary for Granny's sister.

Lizbitty is correct, you need to find your great aunt's most recent PoA document. This info is contained in it *if she included it* when it was legally finalized. Usually there is clause in a PoA that accounts for incapacity of the assigned PoA. Hopefully your great aunt named an alternate at the time she created this doc.

You said, "At this point I'm my granny's POA..." FYI you are not your great aunt's PoA on behalf of your granny unless you were named as an alternate in your great aunt's document. Only your great aunt had the authority to make this change.

Who has your Great-Aunt named for her backup POA? On the POA’s it lists the primary POA, and a backup should the primary become incapacitated.

Best to find the document and see for yourself.