Good observations. I’d say it might be a button. Looks a little big for a .223 hole in any case.
Not a button.
High quality men’s suits do not have button pockets on the outside. They will have unbuttoned pockets on the right side for a pocket square embellishment, flag pin, boutonniere, etc.
Trust me, Trump would be sporting a Brioni or custom made suit. Men who can afford them are going for aesthetic, not utility.