The intention is that after an installation users get a warning when there are known vulnerabilities.
No matter how this is implemented.

Think about the following scenario:
A user installs the current version of an application (like web browser), but the application has vulnerabilities.
The daily VulnDetect will start in some hours.
Now the user browses in the web and gets infected or hacked (the vulnerability is abused).
And after that he can see in the list of installed applications (in VulnDetect) that this software has vulnerabilities.

So the user will be very upset, because VulnDetect does already know about the vulnerability but did not warn him in time!
This could really be a problem for VulnDetect.

I also suggested a new tab "Recent Apps" in List of Applications where I see a list of applications that I had installed in the past (so this is a personal list).
The Library that is suggested here I a common library where users can select any app (a common list where users might have installed some apps).