Steam/Sims 4 Deluxe Edition

@fairymeat1020  It sounds like you added the Sims 4 Demo to Origin, which is a separate standalone (free) product and doesn't have anything to do with playing the game itself.  When you own Sims 4 in Steam, you need to install it through Steam.  The first time you launch the game, Steam should prompt you to link your Steam and Origin accounts, after which point you'll be able to play Sims 4 (the full version) through Steam, with Origin running in the background.

If this isn't working, you can instead refund the game on Steam and buy it through Origin.  I'm not sure why it says you're not eligible, but try using origin.com and not signing in until you click to buy.  You certainly don't need to buy through Steam, and the Origin version is currently on sale for $5 U.S., so you wouldn't be losing money either.

It should be noted that if you refund the game in Steam and buy through Origin, you might need to contact EA customer support to get the Steam version removed from your account.  That's a minor headache too and is probably only worth the trouble if you can't get the Steam version to launch.

https://help.ea.com/en/contact-us/