How to finish edge of tiled shower with metal outside drywall?

If I understand correctly, the question is how to finish the 90degree transition where the metal trim meets the drywall.

First, I would clean up the metal trim. Scrape off or use some kind of adhesive remover to remove any residue. You may need to buff/polish it with some fine grit sandpaper.

For the transition i would use caulk, If you feel it may see a lot of moisture then use 100% mold/mildew resistant silicone. (after painting the wall)

If not then a paint-able caulk (before painting the wall) that would be able to accept the paint color you choose for the wall.