It stands to reason if you are not using Pulse Secure or if it is no longer working, you should uninstall it for no other reason its presence will only complicate matters. Same goes for Airwatch (which may have been installed in conjunction with it) Citrix, Kinoni Epocam or anything else you are not certain about. When uninstalling things always research the developer's legitimately obtained uninstallation instructions, or contact the developer on your own. Never resort to using some generic "app zapper" and never Google for a solution. That's how people dig themselves into a bigger hole.
I am reasonably certain the one Apple file in the second screenshot is no longer needed either. Its presence does not cause any trouble, but in my opinion if something is not needed, you might as well get rid of it.
The point is that everything in those folders will be there only if you want it to be there and are certain you need those files for the software you require. Nothing gets installed in them without your consent, and no legitimate product will hide behind some obscure name. If you want to continue troubleshooting along those lines, repeat the above instructions — start in Safe Mode (which renders those non-Apple system modifications inactive so that you can delete the files), drag anything suspicious out of those folders and into the Trash, or even your Desktop, restart normally, and evaluate.
If you still encounter that unwanted dialog the next step would be to download and run EtreCheck. For instructions, How to use the Add Text Feature When Posting Large Amounts of Text, i.e. an Etrecheck Report - Apple Community.