I have been reading this thread for a while deciding what to do with my brushed link bracelet. I've owned it since the original Apple Watch, and so it built up both daily minor nicks, and some large scratches.
Some videos on YouTube show the process of using a Scotch Brite green pad, either dry, or in combination with a stainless steel polisher. I used both, but remember using the abrasive scotch brite pad makes sure you're not "polishing" the bracelet to a shiny finish, and instead giving it the brushed look.
Below are images of the final result. I don't have "before" shots, but my bracelet was pretty beat-up before I started. It took about 20 minutes of light rubbing with a Scotch-Brite pad in the same direction as the grain.
https://www.avforums.com/attachments/img_7906-jpg.786661/ https://www.avforums.com/attachments/img_7909-jpg.786662/
Sorry just seen this.Will try and get some pics up later if not tomorrow. Im still happy with the way its wearing. To be honest I haven't polished it in well over a year now.