I'd want carpet with a nice thick underlayment.

Kids love fluffy high-pile Moroccan rugs :)

I had been thinking of possibly vinyl plank with area rugs. I decided to do the "kid test" with pictures of a couple ideas, and they picked vinyl plank with pink/purple rubber tiles instead of area rugs. Sounds cheap, durable, and doable to me, and we can switch to carpet or area rugs when they're older. :)

you could also do a decent wood look laminate. I would stay away from anything of color because she won't be 5 forever! Besides, just get a pink rug to go over it!

I'd install some lovely wood-look tile in a gray shade. Then add whatever colorful area rug you want. The gray will be neutral and grow up with your girls. Much easier and cheaper to change a rug than flooring! Tile will not stain, so it can take mishaps better than wood or carpeting.

I'd install continuous flooring through the entire level and add a rug to their room.

I like the idea of the gray wash wood laminate or vinyl floor as a base too. I tried those rubber tiles once for an entire room. It was a bit hard to get them squared because they shifted as you put them together. They made a nice play space for the middle of the room, but did not install well wall-to-wall in my experience. I do think they would make a nice "rug" your base floor and can be easily swapped as the kids grow.

Inexpensive grey toned laminate and a soft (washable) round rug in the middle of the room.

Kids play on the floor and a nice harder surface is awesome for them to play on. Luxury Vinyl Planks or Tiles (LVP/LVT) is a good compromise. Cannot be ruined be water which is always a possibility is a lower level bedroom.

Even girls like to play cars sometimes.

cork is a great alternative too, we put that in our kids playroom /workout room