I have two SDC and live with them 50% of the time. I also prefer a tidy house and DP works nearly six days out of seven every other week, as well as longer hours than me so it’s a struggle to convince him it’s important and equally that it’s important for the kids when he wants to enjoy time with them not spend it by mithering them to clean their room.
With some training you can, without Dad’s involvement, get them to put things away. Routine helps. E.g. if you’ve come home from school, bag goes here, coat goes here, shoes in the box. Laundry goes in the laundry basket and so forth.
You don’t actually need Dad’s permission for that, you just need to make it clear to the kids that if you do this, it means we can do that (together). With ours they’ve worked out they get more playtime if they’ve done their chores and so they just do them.
But you will need to drop your standards. I don’t fret if the kitchen is tidy, the dishwasher is loaded and the bathroom is clean. Toys everywhere are inevitable and putting them in a smaller room just means that they will spread. I point blank refuse to hoover or tidy the kids bedrooms because they leave stuff everywhere, so Dad does it, gives them a telling off, they keep it tidy for a bit. It is chaos after a couple of weeks.
Your own children will have toys, playmat, bouncers, whatever - downstairs and you’ll need to adjust to it. Life with kids is chaos about 75% of the time. The rest is when they’re in bed. You can use this to your advantage, DD can you take your Lego upstairs so that the baby can’t swallow it - kids seem to understand harm and consequences like that better than just ‘your shit is in my way’. Kids here know if they leave lego out it’ll go up the hoover, so the treasured items get put away.
What you need to work on with your partner is partnership. Who will do X, who will do Y, and what that leaves. What that leaves is the stuff you will do if you’ve got the energy or will learn to live with if you don’t.
if you can’t live with it, everyone else will be miserable.
declutter all toys and clothes before baby comes, make things as easy and as obvious for the kids to put away as possible - show them what you want for the first few times, praise them.
but honestly, it’s hard enough trying to work, do pick ups, cook dinner, homework, reading, bath, bed. Without adding show home standards into it - you’ll set yourself up to fail and you’ll be upset by it.