Is this a recent change? I did have Mass Effect Legendary Edition (which was also through origin) up and running a few months ago thanks to Lutris. And I did get NFS Heat through Steam and it also boots up Origin and seems to work okay.
I would check out Lutris if you haven't. The Sims 4 is popular and so someone helpfully created an install script to get it running with Lutris:
I recently installed the Steam version (which in turn also installs Origin inside the prefix to run the game) and it ran just fine. Not sure what issue OP is hitting.
After my PlayOnLinux setup stopped working a long time ago after some Origin update (and several retries afterwards), we tried running the Steam version of the game using Steam's Proton environment and we could start the game only once and then it stopped working again. If you check protondb there seems to have been a regression two weeks ago.
The frustrating part is the game itself would be working like charm in Wine but the stupid launcher app keeps getting updated and is doing all kinds of complicated DLL and system calls although all it really needs to do with respect to "Sims 4" is to check your license and start the game.
So even if you get the game running for some time, ultimately, "Origin" will stop working one time or another.
Not sure it helps now, but I believe there's a (buried) setting to keep a game from updating in steam. Of course the vestigial Origin launcher may not really respect it. And you can force a specific proton version.
I actually kind of loath constantly updating single player games. It usually breaks my working install.
I would check out Lutris if you haven't. The Sims 4 is popular and so someone helpfully created an install script to get it running with Lutris:
https://lutris.net/games/the-sims-4/