I think a first-time DIY effort is as likely to make that worse as better.

If you really want to tackle this, go to a thrift store and buy some cheap thing with a similar stainless steel finish - a toaster oven or something. Mar it in the same way, then try using different grades of fine sandpaper with the grain to see if you can make it any better. There is a good chance the end result will look bad, like not only did you scratch up a bit of the finish but you then messed up the whole area around it.

https://www.bobvila.com/articles/how-to-remove-scratches-from-stainless-steel/

You can buy a stainless polishing kit. But, those are just the first of many marks of use. You aren't going to break that out every time, so maybe just chill, and let the patina develop.