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I am not sure what the finish is. Probably some sort of acrylic. You might try some of the plexiglass polishes and see if that helps. Otherwise a good car cleaner wax has a bit of polishing compound in it too. But both of these will probably remove the "wet look" you have. Sort of the price you pay if you are going to try to polish them.
The other alternative is to try something like Pledge which will just temporarily mask the scratches and you will probably have to apply a coating monthly. Same with swirl mark removers. They are basically just silicones and/or oils.
Give your Service Center a call and ask what they use. When I took delivery there was a few minor scratches on the center console. While we were filling out the paperwork a tech came out with a tube of some kind of polishing compound an rubbed them out in a matter of seconds. Unfortunately I didn't think to ask what they were using.
My car had fairly severe scratches in the wood. My wife is quite crafty and literally sanded the wood down and refinished it to remove the scratches. It can be done.
Be careful. The timber veneer is only .5 mm thick! I have no idea how thick the varnish layer is, but my guess is very thin.
I know, because I made my own trim on substrate supplied by Tesla.