I have a parquet floor. I have been using a plastic underlay for years and do not drive directly on the parquet. The castors do not scratch the parquet floor as long as no paper clip, stone or other hard object gets in between. My plastic pad also prevents the office chair from rolling away unintentionally, as the castors glide very well on a parquet floor.

I've been sliding around on a parquet laminate for months - without any visible marks. I don't know about wood parquet.

I have a tile floor so unfortunately I can't help you.
greetings