New cat left his safe room before we had the house ready for safe exploration, has been hiding under a couch but exploring a bit; how to get him back/adjust?

Hi there cool cats and kittens,

tl;dr: our new cat ventured out of his safe room when we weren't looking, and not readied the rest of the apartment for his shenanigans to be safe yet. He's now hiding under a couch and has been for a few days, though he comes out to eat, use the litter box and explore a bit. Can/should we get him back to the room to "reset" and introduce him to the rest of the apartment properly, after we've finished cat-proofing?

My wife and I recently welcomed home our first cat, Mephisto. His backstory: he's a ~1 year old semi-feral domestic shorthair (looks like a Bombay -- yellow eyes, black coat, tiny patches of white in his chest and inner ear-- so maybe a mix?) who was going to be a TNR by our neighbor who takes care of the feral cats that live in our building's garden, but who was friendly and comfortable enough around humans that our neighbor and us decided to try to give him a home before the cold months hit.

We talked about our enthusiasm to adopt him with our neighbor, and she said it'd be a few days before he'd venture into the trap and then she'll also have to see what the vet said, so we thought we had time to do things like block off the kitchen and secure some high shelves and cables. For better or worse, everything happened very fast (he's very docile and healthy!) and she was able to trap him, get him to the vet and have him ready for us within 24 hours!

She came over with him in a crate, released him into his room (which is close to our home office and on the way to our bathroom, so there's plenty of traffic but not too exposed,) and for the first night he was hiding in a tiny corner of an open closet in the room; but overnight he found his litter box and food, and come morning we found him chilling in his bed, even! For the following couple of days, we would feed him, play low volume classical music for him, and spend some time reading to him. We left the door of that room open during the day so he'd see us go about our day from his room, and he was even okay with us stepping into the room and going to the bathroom. On the third day however, we made the mistake of leaving the door open while we were on the other side of the apartment having dinner (which we had done the previous days and he'd just stayed put,) and lo and behold when we went to check on him, he was nowhere to be found! We eventually found him on a windowsill where we had a lot of our plants, a lot of which are toxic for cats

Since he was amidst all these potentially poisonous plants, we freaked out a bit but tried to keep it gentle and patient, hoping he'd hop out on his own, but after a few hours, as it got deeper into the night, we decided to just start moving all the plants we could grab to our bedroom, which he took with curiosity, but he was sitting on top of a big tomato plant, whose leaves apparently aren't good for them, and after much hesitation, we tried to grab him. Throughout all this ordeal, he was just curious, not hissing, no signs of fear, but when we tried to lift him he did freak out a bit and hissed and we immediately scaled back. When 3 am hit, we resigned ourselves and just grabbed all the fragile stuff we could from the rest of the apartment, and passed out.

The next morning, he had ventured out not back to his bed, but under a couch in the living room. He had peed on a plastic tray where we put shoes (clearly trying to find a litter box, but hesitant to go back to his room which had been open all night?) Since we're new to this, we decided to roll with it that day and brought his litter box out closer to the living room, and fed him where he was, under the couch. Since then he's been chilling under the couch all day (I got him a self-warming mat and put it there, since it got super cold lately and he has a cold already) and he comes out to use the litter box and eat in the evening, and he explores all night. When we're awake, we let him roam and say a firm "No" if we ever catch him going somewhere unsafe, and he responds well enough to it, and as the days go by he goes out more and more when we're still awake, but bolts back to his hiding spot whenever we approach, especially if we catch him in the room where we had that scary night. For the past two nights, he even seems comfortable going out while we're watching TV and groom himself on top of a chair across from the couch! Or he sits on a chair in the dining table and chill while we're around. But, again, if we move, he'll tense up a bit and start heading back to his hiding spot slowly.

We tried to make his room more enticing, spraying feliway on the bed that's there, leaving food there at the same time each night and morning (which he's found!), putting some safe plants by the window in that room so he knows there's a spot to chill there too, and also another litter box. But if he ventures to that room, he will go back to the hiding spot whenever we start moving in that general direction -- we thought he'd just "discover" this very cool comfy room and we'd eventually be able to just close the door so he learns that's his spot for the night, and he can roam all he wants in the rest of the apartment in the evening/during the day, but maybe that's naïve?

At this point we're of two minds: he seems to be making progress, we continue to cat-proof the apartment (we needed to do some less-than-fast things like set up a missing door and bolt some bookshelves to the wall, so it'll be a few days still) but we're so nervous to leave him out unsupervised as he gets more confident in the meantime -- we've taken to just taking turns spending the night out in the living room so we can keep an eye on him if we hear any shenanigans, which means we don't sleep much really, so for our own mental health, we'd sleep much better if he were to be in his room at night, and then leave him free to check out the apartment during the day when we can teach him what's okay and what isn't (I've only owned a dog before, so maybe I'm wrong thinking that a firm, non-hostile "no", or even the idea of correction, will work? He seems to stop what he's doing if one says no! And we try to give him treats when he stops, too.) On the other hand, he seems to be slowly more comfortable around us -- right now, as I write, he's sitting across from me in the room, looking in another direction, finally out of his hiding hole, which is a first during the day time! So we're hesitant to do things like literally just lift him and put him in his room at night, or block out his hiding spot when he's out exploring, as that may either nudge him in the right direction, or set us back in gaining trust?

Sorry for the long post, but really curious to see what you guys would do; as first-time cat parents we feel like we're straddling the line between spoiling him and giving him a good life, and don't want to err too much on either side with this very early imbroglio!