I hate bathroom rugs - they get very , very nasty, very very quickly! A good bath mat to use when getting out of tub or shower, is fine as it can easily go in the washer. If the floor is truly cold, get a larger area rug, but do be aware of water that could damage it.

Since it’s a bathroom purchase a big outdoor rug that can sustain the tracking, water and moisture. You’re able to put this in a washer

Your bathroom is larger than mine but I have a fluffy white bath rug from target that I love. It’s big enough for the double vanity. In fact, I finally found they had it in stock again so I could replace the one I bought several years ago. It’s non-slip, and I have put it in the washer and air dried it many times with no problems, so hygiene is not a problem.