OP, you and your mum are about the same age as me and mine when we bought a house together. We are tenants in common with my share slightly more than hers.
Two years in she had obvious signs of dementia, and for the last ten years I have dreaded her having to go into a home as she became worse and worse, and I've picked up the pieces. It is very hard when you live together to not start caring, and then your life, career, and whatever else starts going down the pan.
Thankfully my mum is now receiving palliative care at hme, and her share of the house will not become an asset for the council.
I urge you not to do this. It doesn't matter if you're tenants in common, the local authority may well come after her share of the house if needed for care costs. It's no longer the case that if a half (or whatever) share was put on the open market it would be worthless because a prospective buyer would be buying a bedroom, shared kitchen, living room, bathroom etc. The local authority can say they are willing buyers and work out a value accordingly. They can then put a charge on your mother's share, and if you ever sell afterwards they can take her share.
Which to some may sound reasonable, but if you've ended up caring for her (and being in the same house will encourage adult social care to leave you to it), then find at the end you've not been able to reach your own potential, you'll be left high and dry.
I'm definitely projecting a bit in this message to you, but I'd urge you to look beyond the short term benefits of this set up and look to the long term possibility of care and all it entails.