Can y'all help me identify which specific software added an "item that can run in the background"?

You could poke around in /Library/LaunchAgents, /Library/LaunchDaemons, ~/Library/LaunchAgents.

Nothing will necessarily say, "hey, I was made by Corsair Memory."

You can run EtreCheck which will show you what you have installed, but it may not be able to tell you what is starting that background process.

That name shown in that dialog is the person or entity that signed the software certificate. That may have little public relation to the company that developed the software.

but that, it seems, is a Ventura bug that hopefully will be fixed in the next update.

Could be, but most likely is poorly written system modification.

I have several that only put up a notification when initially installed. One theory is the developer installs the background process every time it runs instead of only once.