How would I go about moving my stuff to Steam?

malvonos  You can't move your EA-owned packs into your Steam library.  But if you want to play through Steam (with the EA App running in the background, as is required), you can uninstall Sims 4 through the EA App, download the game through Steam, and then download your EA-owned packs through the EA App.  Everything will load as if you owned it all through Steam.  You'll of course need to link your Steam and EA accounts as well.

This all has nothing to do with your saves or other user data, which should be intact and ready for you to use once you've switched over.  The content is in Documents > Electronic Arts > The Sims 4 in any kind of install.