Re: Library not synced between PCs.

@kittycatm3w  No, your in-game library is stored locally on your computer, not on EA servers.  EA does store anything you upload to the Gallery, but library items aren't uploaded automatically.

If you'd like to share your library items between computers but don't want to upload everything to the Gallery, you can copy the contents of Tray, in Documents > Electronic Arts > The Sims 4, back and forth.  This is where all library data is stored, and the files are transferrable between computers and between accounts as well.