I'm not sure it's such a big deal. No official is going to do much more than maybe give him a fine about it. F1 is just butthurt that drivers may advertise products unlicensed by them.
They're apparently targeting watches on the track too now, with Hamilton immediately protesting by wearing three of them at a time during a presser... https://www.yahoo.com/lifestyle/lewis-h ... 00346.html
Good on him for taking a stand. It's just a money issue disguised under a safety pretext.
The way they handle watches is just weird anyway. Those racing gloves with watches printed on look ridiculous, and the way someone just shows out of nowhere and slaps a watch on the drivers the moment they step out of the car is just comical. (those Richard Mille, especially, look ugly, gaudy and heinous... talk about more money than taste)
As far as calling it vanity, I'd say that all these F1 drivers are full of themselves. They're young, mostly naive when it comes to anything other than driving fast, given all the attention in the World and given literal tons of money. People have gone insane with less.
Within that scale, however, I don't think Hamilton is the worst.
I also doubt the claim that he just gave up and is sitting the season out.
He's certainly on a low and has to adjust to competing with the midfield instead of running races in clean air and standing on the podium every other weekend. I think he will adapt. He is still a (highly paid) professional. He probably has to work on the mental. It's hard to get down from the dizzying heights he was at.