I wish you only the best. I believe you will do right by your aunt and be a point of contact. I would personally not pay for anything; the private NH will add to bill. The public ones will provide most things for free (yes, they won't tell you that but they won't leave your aunt with matted long hair if you don't pay for a hair dresser).
Financially I would let the nephew sort it out, and honestly, worry about what happens after she dies when she dies. It is not your responsibility. But you will be able to put your head on the pillow at night and know that you are doing the moral, the right thing. A visit here and there, a bunch of flowers at christmas, checking in on staff, you can be of such help to your aunt if you choose to be. You don't have to do it - but you want to do it.
I know of lots of people that had no next of kin - some never had any visitors for years. I know of others who had neighbours come in now and then just to say hello. And believe me, I knew more than one family who had a niece or nephew or cousin who dropped in a lot, but had nothing to do with their fees or finances. As another poster said, no one can force you to do anything, or to take responsibility for anyone. But you can do a little bit as a human being. Most staff in NH will nearly adopt them (especially the public ones, the staff there generally stay for long periods of working). Plus a lot of ativitities are free, PT, ot, AND especially SW. The fact they have no hidden costs will be of benefit to your nephew (who cares) but will be of benefit to your aunt. Private may not take aunt if there is an issue with payment, so I would assume public NH will be looked at.
Just be a little careful about your involvement. the NH may try to drag you into meetings about care plans, and decisions, etc. It behoves them to be as compliant with best practise as possible. You can be firm and say I want no say say in her care. And stay firm.