I finally feel like I have the balance now but it's largely due to my children's ages and the fact I work very flexibly. It's the school run for my primary child I find the most limiting tbh, but that stops next year. They are 14 and 11.
Work full time - WFH, flexible role, own my diary
Keep a tidy house - DH and kids do their part, cleaner
All the washing - DH's job
Help with homework - eldest doesn't really need help now, and is a maths whizz so helps youngest. Potentially looking at a tutor for youngest, but his homework is quite hands off.
Cook fresh healthy food - UPF (and reducing it) has been my obsession this year, I'd struggle to manage this without WFH I often put a loaf of bread on during a break, that kind of thing, no commute makes it easier to cook from scratch each evening. DH cleans up and makes lunches (DS does lunches too)
Attend school events. - see point one about job flexibility
Take to clubs - we car pool
Play woth children - ages means ours don't "play" much now but we do board game nights, have more shared interests like films, go to the gym together. So this gets easier.
Food shop - I do this first thing Wednesday morning (work flex so would just work the time back)
Sort Christmas/ birthdays - spreadsheet, I start in October, similar to above I chunk it up and often do some admin first thing before I sign in to work.
Life admin - as above, and split with DH
Me time, I play a sport twice a week and go to a couple exercise classes M-Th usually after I've made dinner. Kids are up later now. And tbh weekends are pretty chilled, hence me lying in bed MN-ing right now!
I'm hoping this shows some things get easier, but appreciate it's harder when working out the house, I am looking at doing so again when youngest starts high school though.