What is the file system name of the executable shown in the upper right of the Raspberry Pi's panel? See the attachment below.

When clicked on, it displays a menu with two items: "Show Updates" and "Install Updates". It asks for a password when "Install Updates" is chosen, but no action is taken because the account is unprivileged. I would like to allow that one account to only update the system but not grant full root access to everything, just that one program.

I've looked at the output of ps before and while having the applet active, but can't guess at it as even a diff shows nothing.

I hope it is possible to add just that one item to /etc/sudoers or, if absolutely necessary, in polkit so that the unprivileged account stays unprivileged except for that single applet. What should I look at?

Attached Thumbnails

 

The documentation of the applet or, failing that, its source code?

I have no idea what that applet is, but my guess would be that an entry in /etc/sudoers won't be sufficient. Some PAM/polkit magic more likely.
I see 3 different polkit tutorials here

Where is the applet itself though?

That's the information needed to feed to sudoers or, if absolutely unavoidable, polkit.

If you cannot find that out you will have to wait for somebody who uses Rpi OS and this exact applet.
I'd have thought somebody who's been using Linux(Questions) for 17 years would be able to come up with more info.