Little and often genuinely works here. Only 3 kids, but one is only a few months old and we home ed so are here a lot, make mess etc.
Dishwasher and tble dryer for sure. The latter I only got this winter and it makes such a difference at this time of year.
DH does bedtime while I tidy downstairs and put everything back in its place. I don't bother tidying toys etc during the day, but I tidy and clean the kitchen and stack washer as we go. When the dishwasher wasn't plumbed in I would wash up after every meal before moving on so it didn't get left. Often with a baby on my back.
Upstairs is a mess normally, the kids' rooms are their affair on the whole. Bathroom always clean, give it a spritz while the kids are in the bath. Washing every other day unless basket is full.
Have a cordless Hoover to make it easy to whip round every day, get crumbs etc.
Don't have too much stuff. Am ruthless with what gets kept. We have a fairly small house and I don't want it full. Use the garden, kids booted into it at every opportunity.
I can't relax if we are in a mess downstairs, so have just had to find my own way. Little things like cleaning the kitchen while my evening tea brews, not going on phone until dishwasher unpacked in the morning etc.