System software from developer "Apple Inc." has been updated.

Don't allow it.

Apple "System" software comes to you via a software update, or via a silent push (e.g. MRT, XProtect, Camera RAW, etc.).

What you have shown is software attempting to masquerade as Apple software, and you are correct, Apple software is codesigned and would not cause this to appear in the Security & Privacy panel. I have never seen this in any of my recent macOS installations since Mojave, so I too am calling foul.

christiangenco wrote:

Is it safe to allow this system software?

Yes. The developer name comes from the secure certificate. This is definitely software from Apple.

I would think software from Apple wouldn't need my permission.

I don't disagree with you. Unfortunately, Apple software is quite buggy and has lots of problematic user experience issues like this. These kinds of problems make such questions even more difficult to answer. I have to try to explain to you that the software is safe because you should trust Apple's security. But these kinds of bugs would make any reasonable person less likely to trust Apple's security. So what do you do?

You can search the web and see other people who have encountered this same problem. You definitely aren't the only one. Unfortunately, I haven't seen any of those people actually know how to resolve the problem. I do know how, but it is fairly difficult and involves using the Terminal. I can tell you how if you want to try. I have another method that is much easier, but Apple's forum rules prevent me from mentioning it because it my own software.