aww…too cute for words!! I am such a sucker for lop bunnies- and your bunny is adorable! What is your bunnies name?
For flooring you could also use Coroplast- it is what is used to make signs- it is like corrugated cardboard- but it is corrugated plastic- so there are 2 layers with “pockets” inbetween. It is possible to trim it so it has an edge- you just cut thru the top layer and leave the bottom intact and it will fold. It might be trickier to use in a closet and it won’t be as flexible as linoluem to get into place- it is pretty stiff. And it is a pain to cut- at least for me it is- I had to find somewhere in the house to lay the sheet where I was not worried about accidentally cutting thru completely and cutting the carpet- so I had to cut it in our basement. It is great stuff but if you are looking for something easier- it may not be your first choice. Plus we bought a sheet from a local sign shop and it was inconvenient to get home in our car- I think a sheet is 4ft by 8ft- and it does not roll at all or bend much.
Another option would be sheet vinyl- I use it under my bunnies pens. It is sold on a bulk roll at fabric places, I think other people use it to cover picnic tables, tabletops, etc. It is clear or tinted clear- and it rolls and cuts easily. I do lay fleece blankets over the vinyl since if it wrinkles the bunnies will usually chew the wrinkled area. But it is so slick that is about the only way they can get their teeth into it- at a wrinkle or an edge. It comes in different thicknesses- and the thicker the better- less likely to wrinkle. It is pretty inexpensive maybe about $6 a yard or so- and I always get coupons in the mail from Joann Fabrics where I buy it from. I do end up replacing it about every 6 months or so.
If Cotton and Schroeder ever decide to live together full time I might consider making a tile floor base with nice tile, grout, etc. But I would not recommend that with a young bunny that has not been fixed yet. Hormones can cause marking behavior so it is best to have something completely cleanable until the bunny is more “settled”.