Only TENNIS SHOES can be worn on all courts.
There is no special shoe type which must be worn on the artificial clay courts and any tennis shoe will not damage the surface.

All these are tennis shoes that have a light tread and generally herring-bone pattern.

However, you will get a better experience of moving and sliding on the clay surface if you have a herring-bone patterned sole and an even better experience if you have one without an instep.

You CANNOT play on any court if the shoe is not a tennis shoe – that’s a running shoe, gym shoe or general street trainer.
All these are general trainers and are NOT suitable for tennis as the tread is too deep and heavily patterned.