We don't. We have tile under the table so a rug is not necessary. We do have pads on the chair legs so it doesn't't screech when moving them in and out.
We have tile too, and the floor gets to dirty under the table sometimes. I prefer no rug but ChatGPT says we need a rug under their dining table table.
I recently replaced the dining room carpet with wood, and I do plan on putting an area rug under the table. I'm looking for the right one, so right now it is bare wood.