I am a SAHD to two DCs, now aged seven and four. Have been since shortly after DC1 was born.
It's a bit difficult to compare because I don't know how your DH is coping with his illness and how much it genuinely affects him, but I did and still do everything in the house and to do with the children: all cooking, cleaning, pickups/dropoffs, life admin, laundry. We share bedtime routines. My wife will pitch in at weekends with light cleaning and gardening, or she'll take the bins out if I'm tied up with cooking dinner, but it's essentially a case of she has a job, I look after everything else.
It helped that my wife had to go to the office pre-pandemic when DC1 was younger, so there was no place to hide for me even if I had wanted to. If he's physically up to it, I'd strongly suggest that you WFH less if this is an option for you. But I'd also lived by myself for years before marriage and children and it would have never occurred to me to opt out of basic life chores like cooking or cleaning. It also helps that I am, by a considerable distance, the better cook.
More recently, I've had a lot of personal distractions which could creep and occupy a lot of my time - my father died last year and sorting his affairs out is a gargantuan effort, and I'm the sole carer for another relative in their nineties, in rapidly declining health. So occasionally the washing up will pile up, or the kitchen floor might be overdue a mop, but I get it done eventually. FWIW, I had to spend long periods out of the country when DF died and my wife did not pick up the slack, but employed a cleaner instead.