I ran into a similar issue a while back. What I ended up doing was creating a admin account and then hiding it from the SDDM login screen. Then create your standard user accounts that login from SDDM without a password (You just press enter). Now you can select the user and every steam account is separate.
Only thing I haven't been able to do is get a controller to work on sddm but I haven't really tried yet. 😂