can't quit mail
can't quit mail, wont let iMac shut down because mail is open
MacBook Pro 15″, macOS 12.4
command-option-escape will let you open a Force Quit window, which will let you select the program to force quit before doing so. Keep in mind for Mail any message that is still in composition status may be deleted in the process.
Messages being downloaded as part of POP may permanently disappear.
IMAP and Exchange messages are safer. You may find it worth while to try to see where your internet connection may be hung up.