Puzzle mats are OK for supervised playtime (we have them in our hallway play area but the buns are never left alone there) but left to their own devices, bunnies may chew the mats and ingested rubberized material can cause GI blockages.
It’s not ideal, but we have fleece over vinyl flooring in our bunny room. We have three xpens attached together in there and the fleece is attached to the xpens with binder clips (we’re working on an easier solution for attaching the fleece). We are limited on what we can use because of the risk of staining the vinyl plank floor, so it was fleece or a zillion hay mats.
Some people use super-low pile indoor/outdoor carpeting (Lowes, Home Depot) that is pretty cheap. It does have a waterproof rubberized backing on it though so a determined bunny could potentially get to it. We tried some of this but one of our bunnies is a digger, one is a chewer, and the 3rd kept peeing on it (she has vinyl flooring in her condo plus multiple fuzzy dog beds that she doesn’t chew)