Gonna piggyback off of this. I'd say rather than stages, which can just complicate things. It's just a temporary reduction to Durability loss, durability is something that's already in the game and working with that could hopefully be easier than adding new mechanics. Such as lets say for the first two to three days after washing your clothes their durability decreases by 50% of what it normally does. At this point you're not restoring them, but preserving them. And you could include the need to craft a Clothesline to let them hang out and dry. This could incentivize players to actually keep more than one set of clothes on hand instead of staying all the way through the game with their Class Starter gear.
As it is, you really only see someone keep extra clothes as either a flex or to sell later to a trader. If they had a need to keep extra clothes while one pair dries out, you could have a reason for them to do it. Though, at that point getting soap would need to be easier to create than cloth/sewing kits otherwise many players will just stubbornly not bother until their clothes rot off and then reach for a sewing kit.