Agree everyone has their own strengths.
Indoor things which aren't messy but can be fun:
Ball pit balls in a playpen or paddling pool or tent
Blocks/duplo - making towers to knock down, building different things
Brio (or cheap wooden) train tracks - build complicated layouts
Toddler disco - cheap disco ball online + your own music
Play hide and seek with toys e.g. teddies or a set of plastic fruit
Then if you want some "cheat" crafts:
Google "cut and paste _" with whatever theme you like. It's colouring and then cut/stick. Or use junk mail and order sheets of cheap stickers online to make pictures. Pritt stick is non messy and you can just hoover up the excess paper.
Buy mini cheese + tomato pizza, chop some toppings and let him put them on
I think letting them do housework with you is great BTW. It is fun for them, it's cute watching them do adult stuff, it gets them in the mindset to do it when they are older, it counts as interaction and the housework gets done.
Letting him loose with toys that make horrible sounds and lights is also fine. It's good for him to entertain himself sometimes. Other good toys for this age are a shape sorter, stacking rings set, stacking cups. If he won't play alone, try sitting near him watching with a cup of tea. Gives you a rest at least. Then over time you can "just pop to the loo" or "just get this washing out" and slowly increase his periods of playing alone.