Could also be from some defunct offshoot off the freemasons or some other adjacent secret society. The rosicrucians are perhaps most well known, but secret hermetic societies were fairly in-fashion during the renaissance. Given the secrecy involved, it's probably very hard to know what is and is not (and has been) a significant gesture.

I'd also personally not be surprised if hermetic symbolism cropped up around the Medici-adjacent artists in particular, given the Medicis' proximity to Pico della Mirandola who was fairly important in bringing together this new mix of christian, jewish, gnostic and neoplatonist mysticism.