The thing is, Medicare, which is not income based, will pay for lots of medical things, but it absolutely will not pay for a nursing home except under certain limited situations and for a certain limited amount of time. And since somebody must pay, they immediately ask the individual to pay. If your grandmother who gave you this large amount of money didn't give you all her money, she'd have to pay for her own care after any time that Medicare would cover, using her assets. If she owns her own home, they can put a lien on that home to pay for some of the care though they will not take it until she has passed. Once she's paid out all her available assets such as money in the bank, the necessary care would begin to come from Medicaid, which is income based.
But to qualify for Medicaid, you must be low income. As someone said here, you cannot expect the taxpayers to pay for her care so that she can leave her grandchildren well off. In the case of qualifying an elderly person for Medicaid, there is a "look back" period, as you know. What you do not understand is that if there's nothing that Medicare part A and B is paying for that is medically necessary right now, then you have no need to apply for Medicaid.
There's no reason to apply for Medicaid right now because there's no need to do it. And, if you did apply, she'd immediately be found ineligible due to the large cash gifting she made to you, which would be considered a voluntary divesting of her assets to enable her to qualify for Medicaid. They'd say, no, not only does she not need treatment under Medicaid now, let's use up all this money before you qualify.
But the point I see here as very important is that you've got a 93 year old person here that you are apparently living with and we hope, caring for. There is NO possible way you can predict what in the world may happen regarding her health in the next two years. You seem mighty sure she's going to be around two more years. She might just fail to wake up tomorrow morning-- then all your worrying about and trying to predict what Medicare and Medicaid and all these situations will pay for or might do was a complete waste of time. Or as happened in the case of a 90 something person I know, they fell, broke a bone, were in the hospital a week, went to a nursing home (fully paid for by Medicare) and survived for less than a month. No Medicaid ever necessary. Or she gets dementia, goes into a memory care unit, which takes the home after her passing. You just can't begin your estate planning when you're classified as super-old, and at this point, there's no way you can specifically predict what your grandmother will need in the next two years, or what exactly you ought to do.
If you doubt this you're more than welcome to talk to an elder estate planner and let them give you some possible alternatives.