Comment 2 for bug 1932328

I'm seeing the same thing after the recent update to Thunderbird 78.11. Ubuntu 21.04 on Wayland. x11 is ok. In my case it appears to be related to the Reminder dialogue opening. Some more details:

Start Thunderbird and make sure the Reminder dialogue does not open (eg by snoozing any reminders in a previous session).
Open a few emails in new windows - everything works as normal.

Now set a calendar entry for a few minutes and wait for the reminder dialogue to pop up.

Icon on dock shows indicator showing two open windows
Open an email in a new window
Icon on dock shows indicator showing three open windows
Close email
Icon on dock still shows indicator showing three open windows
Icon on dock is now unresponsive to left click. Right-click shows the menu listing all the windows you have opened, but is unresponsive and stays on the screen. It goes if you press "Super" twice.

Then switch to Thunderbird using Alt-tab
Repeat until more than 4 windows have been opened - icon show the maximum 4 indicators.
Close Thunderbird using Quit from the menu (ps shows no running Thunderbird processes)
Dock still shows icon with 4 indicators
Left or right click no longer does anything. A middle-click starts a new instance of Thunderbird.

Update: clicking on the Thunderbird Mail application menu in the top bar shows a complete list of the windows you have opened since Thunderbird was started.