Again, they were not properly written to handle being turned off. I have read here that Chrome or an extension re-enables the Login Items. That’s a problem with Chrome.
The Login Items are entirely separate from the Background process Notifications and controls even though located at the same panel.
A Login Item can start up without running a background process. An app can run a background process without having a Login Item.
The notifications are for the background process, not the Login Items. Also, an app can launch a background process and actually start at login without being in Login Items.
Apple provided a control to disable background processes, but that doesn’t mean the app running the background process knows anything about that control. All it knows is when it tries to run its background process, it doesn’t run. Since you told the app to run that process by the mere fact that you installed the app, it attempts to “fix” itself by adding a new background process, triggering a notification.
Those other ways of starting up can be accomplished with LaunchAgents or LaunchDaemons. There are folders by those names in the Library folders that may have the controlling launchd plist. However, the startup item may be embedded in the App bundle. Removing the plist may prevent it from running the background process, or it may break the App altogether.
The Apps need to be updated to work properly with Ventura.
Since Chrome already violates the Apple guidelines that require the app have a method to disable login items from installing, I don’t imagine they will fix their app for this, either.