My apple watch was scratched by the original metal strap.

The scratches in your photo do not appear to have been possible with the watch strap in the picture. You will see the fitting onto the watch case is the pivot for the first link, so it should be impossible for the link to contact the case and make the scratch lines visible in the photo. In fact the scratches at the top/right in the photo appear to be skewed and not even aligned with the expected pivot movement of the links if they had been able to contact the watch case so the scratches must have been caused by some other external object.

I think you need to look for other possible causes of scratching.

You can buy a protective case but it is not neccesary