I only have a few minutes before I head out the door. But try saving a few things - with your Library Panel open and watch what happens!
It should be cloud based. So any device you use ... your Adobe ID lets the things in your Library travel with you. I guess it's kind of like the precursor to LR CC -Cloud based app VS LR Classic. But I love saving my fave styles in my Library Panel - it was just easier and neater than navigating my styles palette. I only keep my Go To styles in my Library. You can use the Library Panel to save lots more than just styles too. Color Palettes, graphics/images, brushes. I keep it streamlined for styles mostly.
Like
@cfile mentioned ... when you create/save a style - it will show up in your Library. If you have a few Designer styles you love - you can simply save them and it will show up in your Library. It's a nice little way to have your faves front and center.