I have Steam as a background service in my Login Items -> Allowed Background Services list. I don't know how it got there. But, it has been there for a long time now. I turned off Steam service yesterday to see what happens and now I think it tries to start itself every time. Even when it's turned on, it tries to turn itself on as it seems.
I don't have Steam installed currently (must have tried installing it maybe a year ago)
MacBook Pro 13″
The answer from P. Phillips worked. Had to do something extra after restarting the mac which was to delete a file named "com.valvesoftware.steamclean.plist".
At a guess, when you got rid of Steam you missed a few bits. I'd contact them for details of what's installed where, so you can remove them.
This link may provide additional insights
Before doing that, make Time Machine Backup is very useful and incase
https://help.steampowered.com/en/faqs/view/30EB-87BF-531F-512D
You are Welcome and thank you too 😀
Especially for the Additional " Golden Nugget " "com.valvesoftware.steamclean.plist" removal and personal citation 👍
Do come back to the Apple Support Communities ( ASC ) in the future, if / or when additional questions may arise
How to remove a background service from Login Items?
