Expansion packs missing from order history?

@KillerRaven125  Are you sure you registered the packs to your current account?  It would be strange for none of them to be listed on the store site.

You don't need to download anything from Origin, or even download Origin itself, but it would be good to check your Origin game library to see whether the packs are listed as owned.  You can do this on origin.com or in the app.  Open your game library, click on the Sims 3 icon, select More > Expansion Packs (or Stuff Packs), and scroll through the list.

If your packs are in fact not listed as owned, you'll need to contact EA customer support to ask for help.  It would be useful to take a couple screenshots of the keys in your Steam library, as well as of your receipt from Steam if you can still find it in your email.  You can upload the screenshots directly to a live chat session.

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

Support is on limited hours right now, with phone calls entirely unavailable and live chat only open from 9 am to midnight GMT.

As for an Origin install, if the packs aren't in your game library, there's no point in switching to Origin, since you wouldn't be able to access them.  And installing through Origin wouldn't change the status of the packs on your store page.  Switching is also a pain because it requires a clean uninstall, including removing the Sims 3-related entries from your computer's registry, before installing a different version; this goes for switching between a Steam and Origin install, or Steam and disc, in either direction.

However, this wouldn't affect your mods.  Patches 1.67 and 1.69 play exactly the same, and the only difference is the internal build number.  The only mods that would even "notice" that are core mods, and there aren't very many.  Even so, a core mod would work fine, it would just throw an error at the Main Menu.