Bug#993152: Found a solution for the problem

[Yury Kotov <koteyur@gmail.com>]

I installed Debian 13 Trixie RC2 and selected Cinnamon during installation.
I encountered the same problem as described and tested both the “When
printers exist” and “When printing” options. In both cases, the icon
remained visible and did not respond to click or double-click actions.

After some investigation, I found that the issue was caused by
/usr/bin/lpq not being installed. Once I installed the cups-bsd
package (which provides that tool) and re-added the applet, the
problem disappeared.

Hope this helps.