Well, Midnight, we can't really say if the buttons on sailor's jackets were purely decorative because we simply don't have any sailor's jackets extant. So there goes the best kind of source.
However on the extant coats we have from the period (which are arguably MUCH higher class than these), buttons are sometimes decorative. But even on those coats, most of the buttons on the coats are functional. Usually it's the buttons on the backs of the sleeves that are purely decorative, not the pocket flaps.
In the Admiralty Slop Contracts, a certain number of buttons are specified. And frankly, buttons are expensive. You don't put them on a common sailor's outfit just for pretty. At least the Royal Navy wouldn't!
So I would expect the buttons on these common men's jackets to be functional or not to be there at all.