How do you see this situation as different from splitting rent with a housemate?

To me, the ethical questions lie not in the situation, but in how you handle it. Charge your tenant high enough rent to cover the full mortgage, maintenance, and renovations of the whole building? Sounds sketchy. Charge "market rate" just because that's what the hedge-fund landlords demand? Sketchy. Find a rent level that accounts for your costs & maintenance of the rented space, an allowance for vacant time, and risk of bad tenants? That's a great way to help people find housing, without being an actual charity, and make more sustainable use of a big space than living in it all by yourself.

The most important ethical obligation you have right now is assuring your family member that you are going to be alright after their passing. It’s clear that your family member is worried by your situation and is hoping that the inheritance they leave behind will materially better it. You don’t necessarily have to lie to them and promise to do exactly what they request, but you can at least agree to give it serious consideration and look into the specifics. More importantly you can assure them that you will work hard to be responsible with your inheritance, assure them that it will make a substantive positive difference in your life, and tell them how much it means to you that they care about you so much. Make sure that you’re spending your remaining time together focused on the moment and not either of your hypothetical futures.

After (my condolences in advance) your loved one’s passing, your most pressing ethical obligation will be honoring their wishes. I know it feels like that means becoming a landlord, but it sounds pretty clear to me that their true wish is that you achieve financial security. This doesn’t mean that you shouldn’t manage a rental property (more on that in a moment), but it could mean anything that provides for your future so long as you earnestly try to use the money responsibly towards that end. I doubt your loved one would be as upset at you learning a new trade or opening a small business that allowed you to provide for yourself as they would be if you became a landlord and lived the rest of your days in financially secure misery. Now is the time to take a look at the price of the low end of rental properties you could run while living in and ask yourself what you could responsibly do with that money to ensure your future stability. That is what your loved one truly wants.

As for being a landlord, it can absolutely be done ethically. I don’t ever aspire to own regardless of home prices and having the landlord live on site is my first suggestion every time I talk about improving rental standards. Seeing issues with their own eyes would hopefully lead landlords to address them when they are cheaper to fix and before they become major problems for tenants. The problem with many landlords is that they’re looking for a passive income instead of a job or side gig. Take seriously the responsibility of providing quality housing at a reasonable price that compensates you for your work and you will genuinely be helping people get away from the worst examples of landlords. Being a landlord can and must be done ethically, and you owe it to your family member to look into how it could be done even if it isn’t a route you choose to take.

On a personal note I’m very sorry to hear of your loved one’s poor health. I hope that they do not suffer greatly. Take what time you can now to take solace in each others’ company and assure them that, while you will grieve mightily their passing, you will be alright after they are gone. Right now their comfort and convalescence is the most importance obligation, later it will be their wish for your health and happiness. Good luck my friend, you will be in my thoughts.