Registering your The Sims 3 CD-Keys (each one valid only once) on an account, at either or, should either unlock some rewards content from (or get you SimPoints that you may spend at) - and will unlock a digital download, in the Origin client, of the corresponding The Sims 3 item.
These will continue to display, whenever you start TS3 from your Steam Library, until you respond with the 'Don't show this to me again' button. The display of your TS3 CD-Keys is an FYI NOT an indication that further registration is required. Any valid game patch from Steam will come via a Steam download, just like the original game download did NOT to be confused with a Store Patch. I suspect any patch offered before you attempt to access should be declined. The Sims 3 downloaded from the Steam Store shouldn't need a patch (at least not before you attempt to access ) this download is locally registered - in Windows Registry - so should run just fine without registering with EA / Origin / / / etc.