Siblings - selfish, deluded or...?

I'm so sorry that you're going through this. I'm going through something similar, so I'll share my experience in the hope that it may help you. My father is very ill with a degenerative neurological disorder. He is in his mid-80's, living in a nursing home because he now needs round-the-clock care. A few months ago he was hospitalised due to Covid. The next fortnight was an absolute nightmare because my sibling told the attending doctors tall tales about my father's supposedly high quality of life. One day, I arrived to find my father terrorised with fear and sporting a bloody nose because hospital staff had attempted to place a feeding tube through his nose at my sibling's insistence.
I'm not in the U.K., so the rules may be different, but here, doctors have final say. So, I had a chat with the head of department at the hospital who then liaised with the nursing home and my father's neurologist. The head of department released my father from hospital after adding a DNR and do not readmit to hospital to his medical notes. My father is now back in his nursing home. He has recovered from COVID but will presumably be allowed to die in peace next time he catches a flu or similar. I'm pleased I was able to bypass my sibling's ill-advised wishes but I'm still heartbroken that my father has to continue to suffer through life because of my sibling's lack of understanding and compassion. So, if you can, try working with your mother's doctor's and the nursing home. It is terrible to see loved ones wither away once their cognitive function declines.

When my FIL was dying from the effects of experimental treatment for cancer; it was obvious to all three of his children and their spouses he was dying.

MIL couldn’t see it at all - all she talked about how was she going to cope (with him with an ileostomy bag) when he got home?

It was obviously denial!

With elderly relatives it has annoyed me being between my optimistic sister and pessimistic mother. My sister would go on about how well Uncle was doing and how there had been no deterioration for months, whilst my mum would moan that my sister was deluded and that Uncle was in a terrible state and suffering.

Imo the reality was somewhere in the middle. No, Uncle wasn't well and had dementia, but he was happy. Both wanted to see what they wanted to see without looking at the whole picture.

Afaik, even if they refuse to agree to a DNAR, the final decision always belongs to a doctor.

I think perhaps the anecdotes & " jollying" are your siblings' ways of coping with an awful situation. The denial is the same - pretend it's not happening and it won't be. I don't think it necessarily means that they really believe that, it's how they cope with knowing the truth.

Sometimes humour is a way of coping with things that are too bad to face.