Dedicating part of the Dressing Room to Chairs is a good idea. Chairs are a purely fashionogi item that have no other anyway, so there's no reason not to do this.
The part about adding a manage button to the rest skill is unnecessary. They could add an equip slot for chairs, which I think would be simpler and more reasonable, but I don't think we need even this. Just having a place to collect chairs so they aren't clogging up inventories would be great.
To prevent abuse, limit the amounts and times someone can recycle.
Once per game day up to 100 times a week.
100 recycle points convert to 1 adventure seal
The items would have to be irretrievable otherwise it's just an infinite sized bag. Rather than that just allow the destroy option on everything; same result. Personally, I don't mind the clutter, it fades and newer players may depend on scavenging.