Some professional signers of the baroque period and later had sweet merch, although I don't believe any of them profited from it directly through royalties or such, only indirectly through spreading their celebrity. It was a bit of a "thing" to have little enamel miniatures of your favorite singer and you could put them on your dress as a pin, on a chain as a necklace, or on the tops of your shoes (like decorative buckles). Luigi Marchesi and Farinelli are the only ones I know off the top of my head who got fangirls enough to merit shoe-toppers. Here is an example of one of those enamel miniatures for Farinelli. There were also plaster busts of signers that were popular to collect, here is one of an unknown man, they were very fragile and very few survived, I don't know of any for opera singers that survived to today, but we have mentions of women collecting them for their favorite signers in satires and newspapers. There were also some direct musical appeals to celebrity from music publishers, like publishing "Favorite Songs of Sig. Farinelli" using singer's names and their famous arias, not sure if that would count.

But for who first deliberately cultivated such non-musical branding opportunities for their own direct commercial gain like "Pickles Nickels," not sure, but there's not really an equivalent in the 17th-19th centuries. The idea of "personality rights" wasn't really there yet. Some vague movement towards moral rights of artistry (like the right not to have your music ripped off and published at someone else's gain) but even that was very sketchy, and depended on where you were working in Europe.