@mariabig Backyard Stuff was briefly free, so perhaps you redeemed it during that time.
For the packs you bought through Instant Gaming, I'm wondering whether they were EA App codes, and Steam just passed along the data to the App, so to speak. It's unusual to see Steam codes for Sims 4 on sale at all. This would mean you own the packs through the App, and while they'd still be usable with a Steam install, they wouldn't normally show up in your Steam library.
For the rest, please uninstall Sims 4 and the EA App with Revo Uninstaller (the free version is fine), as described here:
https://answers.ea.com/t5/PC/CURRENT-ISSUE-Sims-4-DLC-shows-as-installed-won-t-load-in-game/m-p/12942151#uninstall
Reinstall the App, then reinstall Sims 4 through Steam, and download any packs you own in the EA App through that app, but NOT a second copy of the base game. Everything should install into the Steam version's program files and load as if you'd bought it all through Steam.