I've never given that much intimate thought to Esuna! I believe it's the latter -- injecting wellness into a person to fix everything. But I think a white mage might be better suited to answer that question!
I'd love to help you look for any papers or books on using Esuna as a preventative measure, if you're okay with it! I'm sure there's something in the library at the Mages Tower, or even white mages like Cormac or Sabina or Darius would know something, or at least know where to start looking! [...] I'm afraid I don't know too much about the float spell, but I don't see why it couldn't work on inanimate objects, either!