Thunderbird has a new Option that allows you to control what happens when a new message arrives.
Open Thunderbird Options and search on "new messages" and the checkboxes and buttons that are associated with each of these options are all that shows up. I have the checkbox for Show an alert unchecked, but if it is checked you can customize what will appear in alerts when they happen using the Customize button.
Brian - Windows 10 Pro, 64-Bit, Version 20H2, Build 19042
It is better to be hated for what you are than to be loved for what you are not.
~ André Gide