That's pretty rigid thinking around sets of toys.
Toys can become separated and recombined. Lego can be doll food, guns, a sorting game, etc.
Nurseries are bright but not tidy until the kids put everything away with the encouragement and guidance and modeling of the staff.
There is a place for everything in a nursery too.
I noted you mentioned you couldn't find your keys or the remote and there are shoes and clothes missing, or tossed around.
Do you have a dedicated shelf or basket for keys? Remote?
Why are shoes ending up in odd places? Clothes?
I brought up five DCs in a small house with hardly any closet space. Four of them were girls and when they were small we had endless Polly Pocket stuff, tiny Barbie footwear, board games with all their bits and pieces, Lego, Meccano, Lincoln logs, wooden blocks, tons of crayons, eleventy hundred naked baby dolls and all their clothes, stacks of paper, endless bins of markers, paints/ brushes, tea sets, baking sets, dolls house and furniture, toy kitchen, craft sets of all kinds (knitting, crochet, friendship bracelets, paper flower kits, origami kits, beaded hairpin kits, pinhole camera kits, make your own kite sets, make your own lipbalm/ earrings/ stuffed animals/ knotted blankets/ sand layers in bottles, and much, much more), Girl Scout gear. And that was just the 'girl' stuff. There was a massive Hot Wheels car track, large wooden train track set and dozens of trains, action figures, plastic dinos, farm animals, safari animals, Lego models, Boy Scout gear, a guitar or two, air dry clay, baked clay, kinetic sand, playdoh. Disco skates, inline skates, ice skates and guards, knee, wrist, elbow pads, helmets, bikes. Dressup box and costumes for various dance and ice shows. And books, books, books.
It was all recombined and adapted to different games. One day the guitars were dressed as zombies in the contents of the dressup box. Tiny polly pocket accessories were used to give extra ballast to Hot Wheels cars. The dolls house was occupied by numerous action figures with a stockpile of marbles as ammo. Endless combinations and permutations really, and nobody minded the odd bit missing.
When they were older, we also had tons of sports equipment (soccer, baseball, softball, tennis, swimming, hockey, volleyball, Irish dance, gymnastics, and all the crap that went with speed skating). Plus a Wii and a PS or three, an Xbox, and all the controllers that went with all that.
I spent time every evening picking up and organising when they were small. It was nice to have lots of storage cubes, and certain places were strictly off limits - the key drawer, the basket where the remote was kept, my makeup. By the time they were teens, they were trained to keep track of their own stuff.