Hello Mitramonday, and welcome back.
Lovely to hear that you're now settled into your new home and considering re-homing a rescue cat.
In terms of your neighbour's cats, my advice would be that I would really pay attention. If one or more of her cats is very territorial, it could create real problems for any cat you choose to adopt.
One of my own cats is quite proprietorial over his patch, and even though he's neutered, he's got himself into scraps defending his lazy acres. Last year, in a "Johnny Cash" type spat, he lost part of his ear after a bite turned nasty. I have no idea how the other cat fared.
We also have neighbours who have cats, with whom ours get on tolerably well, but conversely, our smallest girl cat is regularly bullied by one of our neighbour's young hooligans, As a consequence she's very wary about when she goes out, and prefers to go out when Moray (her big bro) is out with her. Moray doesnt take any prisoners when it comes to anyone picking on his housemates. He knows it's wrong to pick on gurls.
Is there any way you could cat-proof your garden, so any new cat you acquire can have the run of the outside space in safety? Alternatively, could you consider giving a home to a purely indoor cat? I know you will be thinking: "all that lovely space - what a waste....." but it might be the better option.
It's good of your neighbour to have been so straight with you, as it can be a real issue. At least she acknowledges the potential for, at best, an uncertain situation.