Are fonts part of my Vectorworks library?

Fonts aren’t really part of the library. The fonts  are actually stored in your operating system. So, for example on a Macintosh, the fonts installed on a particular location, while on the Windows machine they are stored quite separately.

Because the fonts are part of the operating system, they don’t have a library type function in Vectorworks. If the fonts are the stored correctly in your operating system, Vectorworks looks to the operating system and then displays those fonts.
Fonts are not part of your user folder and therefore they do not show up on the resource browser.