So does Linnea's geo powers come from her being a Fae or her Moonwheel or Lumi?

I was just looking over her animations and noticed all of her abilities revolve around Lumi, with her bow charge just being something that marks targets for Lumi...

not only that, but her moon wheel story says that her vision manifested after it was swallowed by LUMI??

So, do Linnea's geo powers only enhance her bond with Lumi, or does she actually have the ability to wield geo herself?