Was your mother a coper who got on with shouldering everything and told no-one of the things she suffered? If you have inherited this, and keep hiding your distress, they won't know that you are feeling it, and will think that you are doing fine. They could reach your age and still believe that you lived a charmed life of stressless peace and never experienced anything they might be going through.
Sit down and talk over with them what you can do and what you can't - physically or mentally, as Aveline was asking.
If you are not happy with them moving back, would it be better if they lived somewhere else? If you would like more contact with your other child, have you tried setting a day a week when you phone or zoom them - it doesn't have to be a long talk, but you would catch up on each other's lives and it would make you feel less alone.
If you are generally depressed, have you consulted your GP?
If you like them being there but find it painful and exhausting to stand and cook, or to do housework, what are the alternatives? The AC taking over the cooking? Ready meals? The AC doing housework in return for the board and lodging?
If shopping is a tiring unpleasant chore, could you shop online? The delivery drivers would carry it into your kitchen and are even empowered to put it away for you.
You say - "I'm not great mentally and have been blindsided by a few things over the last few years. My back is basically shot due to medical negligance re an epidural." and "I don't bother them with it" - but you expect them to be bothered by it without being in the know.
Perhaps it is time to start bothering them with it? If they don't know the history of your experiences with that, they will not be aware of how debilitating constant pain and weakness can be.
If you need a walk-in shower but can't afford it, have you investigated how you might be able to get financial help with that, or have one fitted by Social Services? Your back pain may entitle you to something? Of course, you would have to admit to them that you needed it - I suspect that you would find that a difficult confession to make, but tell the ghost of your mother to butt out.