This is pretty much my system. To make uniform work I wash Fri night and into Saturday for clothes and towels, and do bedding on Mondays.
With the bedding you could just do sheets and pillowcases weekly and duvets fortnightly.
Re volume of clothes, they are at an age where it gets harder. School uniform 6 shirts,(because packs of 2), 2-3jumpers/1 blazer, 3 bottoms, expect to wear 2 jumpers and bottoms per week, new shirt daily.
Home tops about 8 T shirts, 2 smart shirts, a couple of casual shirts or long sleeved T-shirt, about 5 hoodies but these rotate. One will be used for a few days then go in the wash before a clean one is started. 2 pairs of joggers, 2 pairs of jeans, 2-3 shorts. PJs 3-4 for winter, 2-3 for summer, wearing 3 nights each. About 10 boxer and home socks.
My daughter has a bit more leeway because girls' clothes are more complicated. Also my kids do not change into home clothes after school, which I think makes everything easier to manage. If they were getting changed after school I would expect them to wear the same t shirt 2-3 evenings as they're only in it a few hours.
Bedding and towels do not go into the laundry basket, but straight into the machine. I empty the laundry basket (clothes only) every single Monday.
You're absolutely right that the number of items they own matters. It helps a lot too if all their things fit easily into their drawers. If they have 12 hoodies and the drawer doesn't shut, everything is harder to manage. My son is autistic and gets very overwhelmed so all his clothes fit into a 75cm IKEA pax cupboard - about 4 drawers with hanging space over.