You ask an interesting question. Polishing is abrasive and will remove the coating like Wyatt explained. Revive is a decent product to try, but I’m not sure how it’ll do against the coating. Think of it as more of a cleaner than a polish.
If you decide to polish, consider a few things. You will shorten the life of the coating. You’re abrading the coating, so there’s no way around that. If you’re not careful, you will completely remove the coating. Coatings are microns thick, so it doesn’t take much.
Keep your coating maintained with ceramic boost. This will help with a fine “sacrificial” layer during the winter. Use proper technique when washing.
Lastly, as an alternative there are products out there that are designed to go on top of ceramic coatings with fillers and such that are aimed at “repairing” damaged coatings. We have used them with good success. Just know it’s a band aid solution.
Polishing the car will remove the ceramic coating so you will need to reapply the coating wherever you polish. You can try revive hand polish first as that will not remove the coating, but I would follow it up with some ceramic boost just to be safe. The scratches you have are most likely in the coating itself (just my guess, but hard to know without seeing any pictures) so a light to moderate polish should removing the coating and the scratches fairly easily
