Why do I keep getting notifications about background items added with Ventura 13.1

This is a known issue. There are several threads about this here on these forums. In one of them a well respected forum contributor who is also an Apple developer tried to explain some of the issues here, but I cannot find this post right now. Basically Apple added a new "Background App" feature to macOS Settings (just ignore this are of Settings as it is not what you think it is and may cause more problems) which is currently broken...plus there is no real information about this feature so app developers have no way of understanding how to code their apps to work properly with this new macOS feature/option. Also, don't try deleting any files as has been suggested by some people one as the previously mentioned contributor & developer has mentioned it will just cause even more problems.

Here is the best post by this respected contributor & developer (they are not associated with Apple, but are just a regular user who happens to develop apps for use on macOS). This post provides the most relevant information about the issue. As a third party developer, this contributor has some experience and insights into how macOS works, and is the only contributor that I've seen currently posting here on the forums with such deep insights into macOS behavior. Only the people actually designing & developing macOS itself would be able to provide more accurate details.

Perpetual "Background Items Added" - Apple Community

Another relevant post from the same contributor:

Perpetual "Background Items Added" - Apple Community

At best you can provide Apple with product feedback or provide an official bug report (the latter requires lots of very specific details including how to reproduce the issue on a clean install of macOS, etc.). Even then, don't expect a fix any time soon. At best Apple will either already know there is a problem or know the feature is not fully implemented yet, or perhaps Apple will provide the necessary information to the app developers on how to properly prepare their apps to handle this new macOS feature/option.

If you read the posts I linked earlier in this thread, you will see there is nothing an end user can do. It is up to Apple to either fix this feature to implement it properly, or to provide the necessary documentation to the developers so that developers can design their apps correctly to work with this new feature.

You can provide Apple with product feedback here:

Product Feedback - Apple

The user may what to follow similar question from another user

refer to link below

Apllication in background - Apple Community

This is an issue for me as well. Not related to the issue P Phillips posted.

thank you for explaining how these "Background Items Added" appeared. Can you also explain how to stop them recurring. They are very frustrating