My dc would often be carried at the times you describe, so they would be physically close to me whilst I did things, reassuring, and “busy” watching but not taxing, they’d often zone out whilst I cooked dinner or did jobs like that.
reading books and reading aloud from newspapers (apart or together)
mine often liked simple, gentle repetitive tasks like shelling peas, sorting buttons, washing fruit, kneading dough, peeling vegetables, polishing shoes, all dependent on age and need of course.
listening to music or playing/practising music or singing
listening to the radio
stories read aloud (by a person in days gone by, or a cd etc) my DC like to listen to story podcasts now and they just ask alexa to play them
simple nursery games like yo-yo, marble, tiddlywinks, building a house of cards, spinning tops etc, all easier if you haven’t had a day full of over-stimulation and flashing toys I’d have thought
drawing, sketching, painting and handwriting practice
sewing, mending, darning, embroidery, not something we do much of now but popular in days gone by for idle hands
leading into knitting, crochet, or even simple games like cats cradle, skipping, jacobs ladder
crossword, wordsearches, number puzzles, spoken riddles, treasure hunts
den building, tree climbing etc outside (usually just to sit in the den or sit in the tree being the point!)
writing and telling stories, to yourself or to each other
Taking things apart and putting them back together has been a big thing for my DC and I didn’t expect that! Lot of curiosity on how things work and what’s inside
being creative, moulding, whittling, as easy as salt dough or as complex as sculpture, most ages can take out the days stress on making something and forming something with your hands
lots of cooking, baking, mixing
bathing would take up a lot of time too
Just some ideas!