You are obviously buying a home you love, so people saying don't buy it so she can't move in, is just daft, what next, buy one without a spare room, no garden so you can't build a granny flat etc...
Say it's a clear no, but tell her what can be done instead & help her to do it.
I was recently in a situation where my ex mother in law came to stop for what was supposed to be 3 days, it turned into 6 weeks.
She has early onset dementia, she has capacity but her short term memory is non existent. You wouldn't think she has capacity though, she had never had a freind, a hobby, never went to groups, nights out, coffee mornings etc, my ex FIL had a high income, he did everything, the cleaning, cooking, finances, she was a kept woman with no understanding of money, doesn't know how to clean or cook she didn't know how to do anything at all & it was impossible to teach her with no short term memory.
She had not been able to stay in her home because she was neglected & financially controlled by her children, so was staying with the final child, for us to discover by chance that this one was at it even worse. A long story short a SW that was already involved instructed she was not allowed to go back to her home or the child's house she was staying at.
It was round the clock care, the child she was staying with slept all day & then stayed up chatting rubbish all night, so for MIL it wasn't bedtime until 4am. I was getting bed an hour earlier every few days, it ended with me sat on the sofa in the dark every night, because it was like putting a child to bed, excuses to keep getting up, roaming about, keep coming in my bedroom, She was incontinent, but not through health reasons, it was because she wouldn't go the toilet unless you told her to, she simply did not want to have to get up to go, couldn't even make herself a cuppa.
I was not sure what I was going to do, because I couldn't maintain this & she had always said that she would never go into a home. So what I did from here, you could do similar. It may seem like a lot of work now, giving her the time & support, but a bit extra now will pay off in the long run, reducing the chance of you needing to provide long term care.
As you say she has had some health problems & has a no fault eviction, first it's important you contact your LA to notify them of risk of homelessness & also adult services because she has a health need & with homelessness she is vulnerable. The next thing is find out where your assisted living complexes are & take her to visit some.
My DD, knew someone that worked in a complex close to us & she said she would give us a tour, I was able to talk my MIL into visiting. My MIL loved the complex, having a restaurant, library, hairdresser, all on site, lots of social areas always someone to chat to, the flat was a brilliant size, she was told we could get carers to go in 3 times a day. One thing my MIL couldn't cope with was being alone, so this assisted living ticked the boxes she thought she wanted, her own flat, independent living, whilst having company & support always on hand.
For my Mil, talking about what she would want in a care package, she was actually asking for what a residential home provides. I found "senior home plus" a brilliant service, who contacted homes (with availability) on our behalf that met our criteria. I was able to talk her into visiting one around the corner from me. I always made sure to use the term residential home, never called it a care home, she never realised she was going to one of the type of places she had said she would never go to.
She was in a room there just three days later, within a week she was settled, she's been there 7mths now & absolutely loves it, she is settled & happy.
Because her situation is so complex, my life is on hold sorting her out, but I'd rather a few months now, than the other option which would have been her living with me & me being her sole carer providing round the clock care for what could be years.
If you did think you could explore these options I'm happy to answer any questions, it's an area I know quite a lot about.
Good luck in your new home when you get moved in x