I won't say that NVDA is not at play here, because it could be, but ALT+F4 is not an NVDA command, and not tied to NVDA in any way. It's a Windows command that the program window with focus when it's issued responds to. If Thunderbird continues to be "hanging about" with something running in the background, probabilities are that it's not NVDA causing this.
I have asked on a tech geek group specifically for professional techs I haunt whether there is a handy PowerShell and/or Command Prompt command or pipe sequence that would allow someone to zero in on whether a process or cluster of processes of a given name are running. It is my understanding that both Task Manager and Process Monitor are, while not strictly speaking inaccessible, not exactly anywhere near to easy to use with a screen reader.
Brian - Windows 10 Pro, 64-Bit, Version 20H2, Build 19042
The depths of denial one can be pushed to by outside forces of disapproval can make you not even recognize yourself to yourself.
~ Brian Vogel