It appears the best bet is to decide what space you’re willing to devote entirely to your rabbit’s permanent enclosure, and then you can rabbit proof/put gates up against any sections you do not want your rabbit wandering around when you allow for free-roam time. At the minimum though, the space you dedicate for him does need to have a rug and, anticipating little room/clutter/not being able to rabbit-proof the entire space, be spacious enough to facilitate exercise over several hours of restriction time. Use of vertical space would be really helpful, so you can consider doing a more complex build with grid cages.

Here are some thoughts around that (please note this directs to a rabbit forum which is not exclusive to pet rabbit-keeping): https://www.rabbitsonline.net/threads/need-help-deciding-on-which-nic-cube-set-to-get-zip-ties-etc.102559/post-1181862

Looking at the layout, I think your idea is a good one. Use puppy playpen fence of baby gates to gate off the section behind the couch (though I’d bring the couch forward a little if there’s room to bring in the gate in line with that wall). Then if you like you can have supervised free roam time of the rest of the living area and kitchen.

I have no idea if this idea would work for a bunny, but I saw the coolest article in a magazine this week where someone used an open cabinet (door removed, low, like in a kitchen) for a small dog to sleep in. It could enclose a litter pan or have a tunnel fitted in with a seagrass matte for a floor for sleeping and napping. You’d lose a bit of storage space but it would be a smaller footprint of bunny stuff if he likes it. Bunnies feel safe in warren type enclosures at times, so thought I’d mention this idea.