Panel uses duplicate/incorrect icon for Thunderbird when installed directly

Distribution

Linux Mint 21.3

Package version

Cinnamon 6.0.4

Graphics hardware in use

Integrated graphics (UHD Graphics 630)

Frequency

Quite often

Bug description

Due to some requirements involving Thunderbird's setup (theme, etc), I need to run with the latest ESR
version available. So, I uninstalled the version of Thunderbird that comes from the distro's repo, and installed
Thunderbird directly from their repo and used "Add to Panel" to create a shortcut.

When launching Thunderbird, more often than not it will create a 2nd icon entry on the panel instead of using
the one that is already there. In case it matters, I use the "Grouped Window List" applet. Every once in a while
(I'm not positive, but it could be after certain updates get installed by Update Manager and a reboot is done), the
existing icon is used correctly instead of generating a 2nd one. But, most of the time, the 2nd icon is created.
Restarting Cinnamon or rebooting normally does not change the behavior.

Also, every once in a while, the appearance of the 2nd icon changes from the correct one (Thunderbird) to
something else. I'll include a screen capture of that, too - I think an event like a calendar alarm going off in
TB causes this to happen. Normally, restarting Cinnamon will cause the correct TB icon to be restored, but
it is still a 2nd copy and not the existing "master" icon.

Steps to reproduce

Launch Thunderbird by clicking on the panel icon.

Expected behavior

The icon should have an underline drawn beneath it, with the Grouped Window List features like thumbnail preview working correctly.

Additional information

No response

Start by reproducing the launch from the existing panel shortcut on Linux Mint with the Grouped Window List applet and directly installed Thunderbird. Trace the applet's window and icon matching behavior, including the later icon change, and consider the issue done when Thunderbird consistently uses the existing panel entry with its normal underline and thumbnail features.