I think we used to have an orangery... Although we called it a sunroom. It deffo wasn't a conservatory.
Anyways, I also grew up in a house where all mine and my siblings stuff had to be squirreled away upstairs and I wasn't actually really allowed in my parents room either, so I grew up thinking it was trashy and chavvy to have kids stuff visible and just out and about in the living room 🥴 despite the fact that I wasn't happy at all growing up under such uptight conditions.
I'm not like that at all now I've got my own children, and think people who seperate their kids stuff completely off are a bit mean. Mostly because I think it puts odd notions in children's minds that their stuff is an unwelcome inconvenience, and perhaps as an extension that THEY are an unwelcome inconvenience.
My kids stuff is all in the living room and there is tonnes of it. It takes me about 5 minutes to clear it up (probably because everything has it's own place!). Maybe 10 minutes if they've made a den. Although if stuff ends up under the sofa then it's gone until I can be bothered to lift them up, usually once a week.
I suggest having a pretty fabric 'toy basket' you can throw all the odds and ends in you come across in the evening, and if they're missing a piece when they're playing then they can check in there for it.
I also have a gem jar and a gem chart with all the skills I'm working on with my youngest. Once he gets 30 gems, he gets a small prize (usually some toy he has asked for). Helping is one of his skills, which includes tidying his toys up. If I specifically ask him to tidy up with me and he refuses, he may lose a gem. But there's always opportunity to earn it back.
However I am aware as a parent it is ultimately my responsibility to clear his toys away... It's part of the deal.
I would also rather be stressed by visual clutter than have my kids grow up internalising feelings of being an inconvenience. Wouldn't you?