I’m a new sandwich - any advice

If you are low contact, wouldn't you just continue that?
What do you feel it is your job to support her now?

Has she moved with the expectation you will do more for her? Have you discussed it?
There is no set number of times you have to visit, or support you 'must' provide.
Keep your interactions short, get her shopping delivered, don't give her any info to gossip with.

Get shopping delivered, try and condense needs into a regular slot of time and then think of it as charity work. One of my friends does a few hours a week at a food bank, my hours are social care for my mum.

Continue as you are - low contact.

You don't have to get involved with her at all - it's perfectly fine not to be at her beck and call. She's in an environment where there is probably a warden / house manager who can point her in the right direction for GPs, etc. The facility will run social things and there'll be her neighbours for company. If you've never had the type of relationship where you pop around for coffee or go shopping, there is no need to start now. You can be open with her if you wish, or can just leave as is.

Things you don't have to do
take her shopping every week
have her over for lunch every sunday
drop in for coffee after work a couple of evenings a week
take her for appointment to GPs / hospital / chiropodists
tell her any of your family's business

You get the idea

Move?

If it was her choice to move without any discussion with you then carry on as you were before the move.

Continue low contact. Don't help her out.

You don't suddenly change your life. You can decide how much you give of your time.
What you can do is look up services and providers for her.
I don't know who runs it, but there's an Access bus service to the local supermarket. I think it picks up older people, takes them to Tesco and then takes them home. Or you can help with food delivery.
There may be social clubs and activities - where she has moved to may well stage their own or signpost residents to services.

Hi I write in empathy as MIL lives about 15 mins away and it's very similar, down to the gossiping to relatives! In particular they compare and boast about what e.g. children do for them I have noticed!

I think you need strong boundaries with parents / in laws like this. Have a look at the site online called Out of the FOG for ideas, there is also an elderly parents forum on there and one on here too.

One of the benefits of supported living is that, it is set up for them to be able to access support and that can be a good thing.

the more they can do for themselves / set up themselves the better.

I also have a dad in sheltered accomodation far away and he has things like a cleaner once a week, a lunch club he goes to locally one day a week, a warden to keep an eye. He's early dementia and for now it seems to work ok. He has carer's coming in twice a day as well.

I managed to help with an application for attendance allowance so he uses some of this to fund some of the the extra care. This was through using a welfare advice place at the local council who went to see him and did the forms. That was very helpful.

So, my advice is to encourage them to seek support they need locally or else you will end up doing it. In MILs case what we do is never quite right / enough

Fundamentally l don’t think much needs to change, l would stick with the low contact. You already sound busy, she can organise to get food delivered, get taxis to appointments etc.

You do need to provide more information about discussions (or lack there of) around her moving near you.

Do you have siblings or in law siblings locally? I found it helpful to chat to them for support.

You don't have to do anything you don't want to do. And practically anything can be delivered these days.

Oh also I think you are in a good place to start off well as these things can creep up over time.

You do know you don't have to do stuff for her? Just because she has moved nearby, it sounds like you don't have a good relationship, so keep it that way. Just blindly doing everything because you feel you should is a bit martyrish. If she needs help with something like shopping, offer to help set up online shopping with Tesco or similar. I get on well with my mum, but I won't be doing extra food shops for anyone.

You don't have to do anything OP. We're not obligated to care for our parents.

Pick a task and that's it, maybe a bit shopping you can drop off. But really you don't even have to do that.

If you're sensible then you continue to maintain low contact.

If you've ever pondered a move to a different part of the country, perhaps start thinking more about that.

The worst thing you could do is start a caring role, in any shape or form.

Work out what you want.

Ask yourself

How much do I want to see her?
When I see her ideally what do I want to do?
How much time am I willing to offer support? And what support do I want to give if any?

And then make sure you stick to it. She doesn't get to dictate what support if time you offer. It is entirely up to you. What you offer has to be on your terms if she doesn't want that then it's up to her to say no thanks. It does not matter what her expectations are.

Please don't feel that you have to do anything for her if you don;t like her.

You need to look after yourself and your own family. She needs to reap what she has sown. If she had been nice then you could have helped her.

Also, if you start then it will be very difficult to stop, so don't start.

Don't offer to do anything for her. Let her ask. Say no if it doesn't suit you.

Where did she used to live? How often did you see her and what did you do for her before? Where are your siblings and what is their involvement with DM?

If she's made this decision with a view to you supporting her but hasn't asked/discussed it with you then you have no obligation and need to be careful about setting an expectation with her. Can she employ a carer?

What's your relationship like with other siblings? They might be able to travel too, to help out? Or do her online shop etc even from further away.
Can you get a rota going of taking turns to take her to the doctor etc.
Get talking to your siblings about it

Also teenagers can help Gran out. They can run errands, hoover, take her out for walks etc

Make it part of their chores (increase their pocket money if you want). It's great for young people to help out with the elderly.

In addition if she qualifies for attendance allowance or if you can afford it employ someone to do an hour a couple of days a week. Maybe run errands, leave a dinner ready etc Lots of active retired people willing to do this for fairly modest pay.

Don't commit to anything you don't want to OP. What can you easily fit in to your schedule? Maybe pop in once a fortnight for a quick breezy visit? Keep things light, no gossiping.

My PILs live in a retirement flat and one of the nice things about it is that they have a ready made social life if they're feeling lonely. They just need to go downstairs to the communal lounge area and there'll usually be someone there to chat to. Hopefully the same in your mum's place.

Agree that she can get shopping delivered. And taking her for a walk isn't your responsibility.

Thing is with some of this there is an expectation for the OP to arrange this.

The mother could arrange this herself, offering to pay for help,