So, I think it's pretty fair to say that Origin and WINE/Crossover don't always tend to get along, and this has caused some issues for people who happen to have purchased a good majority of their expansion packs digitally through Origin.
While playing around with it today, I may have come across a work around that installs an older version of Origin that seems to work quite well in Crossover!
First, download the legacy client from https://www.dm.origin.com/download/legacy
Launch Crossover and start to install software as normal. I chose "The Sims 3: World Adventures" since it's a little newer release, but any Sims 3 entry should do. Make sure to go to the "Select Installer" tab and "Choose Installer File...", then point it to the origin client installer that you downloaded earlier.
Go ahead and proceed with the install. Once the Origin installer screen pops up, I might recommend UNchecking the "Keep Origin Up to Date" and "Automatically Keep my games up to date" boxes. We want Origin to stay in its legacy versino, after all 😉
Afterwards, you should eventually be greeted with a working Origin window that will let you download The Sims 3 and its expansion packs through it.
Please feel free to post below if the above doesn't work or anything seems unclear.
Hibba