Large plastic dog bed? That’s what my bunny has, with his towels in, my baby is a giant, so a large dog bed would fit 2 fluffy buns in.

A shallow, cheap pillow that you put a water proof case on the inside so it doesn’t get soiled?

I suggest that you try something cheap and homemade first, because my bun has refused all attempts at offering him a bed. Rabbits are very particular about their living conditions: a lot of them prefer to have firm footing and won’t like something pillowy. All my previous attempts at a bunny bed or a soft hiding space were ignored or utterly destroyed.
Our Breintje was moping about the floor getting colder now that winter is approaching: he didn’t want to leave the couch. Luckily I had a scrap of thick fabric left from a DYI project (a leg cover for cold weather use on my mobility scooter). We put it on the ground in his favourite spot, and he seems to accept it so far.

I have Vetbeds for my bun and dog. Easy to wash and apparently very comfy.

This doesn’t meet all your requirements, but I got some machine-washable faux-sheepskin type fleeces at the pet store. There’s no stuffing, so one less problem. TBH my bunny prefers to dig and play with them rather than cuddle with them, but sometimes she seems to like relaxing on them.  If you have something like that, you can set it in a basket or cubby.

My bun loves laying on a microfiber bath mat when it is cold on the linoleum. It is easily machine washable and doesn’t sliDE when he hops on and off because of the skid proof bottom. It keeps him off the cool floor and is VERY easy to wipe hair off and clean.