My 8yo is hypermobile and has ADHD, and struggles with some self care tasks as a result. From your list:
Brush teeth properly - Yes, but we still brush after her once a day just in case and check her brushing every so often with a disclosing tablet.
Shower - Yes.
Wash shoulder length hair - Not fully. She wets it, we add conditioner and comb it out (she has bum-length 3c curls so the tangles are still too much for her. We co-wash hence no shampoo), she will then have a go at combing if she fancies it. She washes the conditioner out herself.
Tie shoe laces - Yes, but only the 'bunny ears' method. It took a dedicated effort to teach this: 10 mins a day, every day for 4 months. She has been able to do this for a couple of years (it was a lockdown goal!) but still looks quite awkward in the way she handles the laces.
Do and undo top button on a shirt - No. The hypermobility affects her fingers and makes this very difficult. I buy the M&S shirts with a velcro top button.
Sit properly on a chair at the dinner table - Ish! Depends on the day! She used to wiggle around so much she'd regularly fall off it. That happens rarely now, but she'll still often sit crouched or on one foot. At school she has a band around the bottom of her chair to help her stay rooted.
If your DC is struggling with all of these things, I would be looking if there are any other signs of hypermobility/dyspraxia/ADHD.
Eg how is her handwriting? Check her movement against the hypermobility checks you can find on Google.