@giveupontoys let me give you a huge hug & a big dose of sympathy. It's hard! And it's even harder when there's so much stuff & it all just ends up being tipped on the floor & then it instantly becomes YOUR problem to deal with.
As DS is in nursery 4 days a week, presumably you work 4 days? So there's maybe a few evening hours in the house, one weekday, and then the weekend? In all of this, most posters have focussed on what YOU should be doing to engage DS's play interest. But presumably his DF is around for over 50% of that total time DS is in your home?
So why is your other half off the hook, scot free, in ALL the discussions about how to manage this?!?
Dads can have a really fundamental influence in showing boys how to play creative play, substitute a car for a missing layer of ice cream without having a ploppy about it, play customer for ice cream, demonstrate that things need to be put back in the box after dumping out, etc. etc.
If you involve Dad more in playing at evenings & weekends, you might find the one day you have DS on your own (?) gets easier and/or you're able to pick up more ideas on how to play with him/what he responds to well & enjoys playing the most?
He may also realise that some of your furniture choices are a proper PITA when it comes to toy management, so you may get some practical support on changes in that area if there's a real world impact for Dad because of those too?
This might sound very idealistic, but do challenge the status quo about why this has become only YOUR problem to deal with OP!
Potentially all of you are not NT...you like order & tidiness & can't work flexibly around missing pieces. DS has a short attention span & needs a lot of gross motor activity to occupy himself. Dad seems to have abdicated himself from all responsibility for child-rearing, developing his children & tidying his home? Whether you are or aren't is - as you've already said yourself - almost irrelevant! What you need to do regardless is acknowledge your current circumstances, how to improve the best bits, and share the load better on the bits you find hard!
From a practical perspective, so much stuff in a smaller house is always difficult. As is having toys in a living room if a lot of your evening/day off time is in the kitchen.
Is it possible to have a very small selection of toys, or some flip books, in the kitchen so he can sit at a table beside you & you can practice 'play' conversations in the same room but while you're doing other things? Other suggestions about having a stepstool, balance board & indoor trampet all sound remarkably practical & well suited to your DS's preferences & your sanity ;)
Good luck OP, and the 'stuff' phase does eventually pass. I really struggled with it too, but remarkably seem to have ended up with 2 reasonably well balanced double-digit DCs, so keep your faith in yourself! Do whatever you need to do to keep yourself sane...but unless there's a big drip I missed about you already being a single parent, I would suggest sharing the load more evenly is a factor which has been much overlooked in this thread generally! 