I think it's more likely that moving to the living facility will be more stressful for the cat, although there should be other things about the situation you might also consider.
Cats generally don't become so attached to people they become obviously despondent in their absence, unlike dogs. However, a cat will definitely miss the familiarity of their person and their routine. But her cat's routine will be lost regardless, as your grandmother's routine will certainly be disrupted by transitioning to assisted living, and worse, in an assisted living situation, there will be strangers bustling in and out, which most cats will not handle well. Meanwhile, the fact that the cat is an outdoor cat means that it probably is already used to her not being where it is all the time.
Of course, cats come in a wide variety, so it may be the case that her cat is unusually attached to her, and so moving it might make more sense. In the end, it is up to you to assess if the cat gets unusually stressed from the absence of its human.
However, I think there are other things to consider. What your grandmother wants very much matters. Does she want to keep her pet? Losing your autonomy is obviously very hard, and holding on to particularly treasured things or beloved pets helps ease a very tough situation.
Lastly, I would consider the other factors of this particular situation, such as the fact the cat is used to be an outdoor cat on a farm. If it were allowed outdoors in an urban area, I'd be very worried it would be hit by a car. Therefore moving the cat may be an issue of the cat's safety. As for the alternative, making it an indoor cat, that would be another disruption to its routine, and as a result, and yet another source of stress. Many cats do not adjust well from being an outdoor cat to an indoor cat as well, sometimes even developing behavior issues due to the boredom.