One really big thing, if at all possible, is to prep tomorrow's dinner while washing up tonight after dinner. So it's much faster and easier to get that done when you both come in tired and hungry and stressed.
Peel veg, defrost frozen stuff, marinade meat, make a sauce to reheat.....lots can be done the evening before to short cut the following day. Things like a curry sauce, so you only need to reheat that and boil some rice - once the kettle is boiled and thrown into the rice, and the sauce is on a medium heat to get properly hot but not burn, you can even take a few minutes to tidy up, get changed, reassure DS about work and help him get started etc.
Have easy snacks in the fridge for when he gets in - food and a drink - so that he can decompress and refuel after school.
Can you meet year head to find out their expectations? As you joined mid-year, they may have explained it to parents at the start, but you don't know these things and it is a new school - you want to both be working on the same page for DS's sake. It sounds like the "no phones in school" but "take a photo of board for homework" don't quite match, so you need to understand their rules and expectations - to help DS to follow these and do what is needed. (That's the message you need to send to YH, you sound like you are in that space already yourself).
We wash clothes all week, and put them up to dry (clothes horse, outside line if dry, or tumble dryer) - but only fold at the weekend (while watching tv together). Dry clothes go into a clean clothes hamper in the kitchen until then so people can rummage if they need something urgently. (We also have a lot of clothes and spare set of uniform, to try and avoid a need for urgent rummaging - but there are times...).
And talk to DS and agree that some standards will slide for a few weeks while you get organised, and settle into the new life/house/school/job. He may need to step up a little to help out (clear his dishes etc). But you both need to get enough sleep, and decent food, to be able to get your new situation off to a good start - and start building from there to where you want it to be.
So maybe the dishes all need to go into the basin and counters wiped before you go out in the mornings, but you will only washup in the evenings with dinner things until everything settles a bit more. Can you use time on the train to do an online shop or other useful admin tasks? Or to take time for YOU to unwind - read a book, listen to music/podcast etc?
And reassure both of you (you in your head, DS explicitly) that yes, it is different and all change is hard, but it will settle down again so give yourselves a (mental) break to learn the new routines and expectations and standards. And also that it is not the end of the world - it is different - but can be good once you get settled back into what is your new routine and find a new normal.