You can use a normal dual-action polisher or just some elbow grease with a microfiber or foam pad (preferably 3" or smaller) and some compound then polish like a normal paint correction, should work well for just haze reduction. There are some metal-specific polishes that you might can use but I have no experience those except for exhaust tips so I kept to paint compounds/polishes.
Could tape off the surrounding black plastics to avoid getting polish residue in cracks & on the trim which would be annoying to clean off, then you could do a final ceramic coating of the whole trim panel if you felt like it. Helps protect it and would also deepen the black color of the sill.
I would not try to sand it since it's kind of a brushed/straight grain finish so I believe you would ruin it by using an aggressive method like that. If there were deep scratches that would probably be necessary, but only in small spots and it would probably take a lot of work to get it to blend back in to the rest of the plaque.
The best way would be to remove the plate from the black housing (there are push nuts in the back). Place a scotchbrite pad on a flat surface and, using a straight guide like another block of wood against the plate, move it back and forth over the pad in a straight up and down motion. You'll get a perfectly straight brushed finish. Just clean it off with some acetone and it will look like new.