I have request to add feature that allows thunderbird to run in background or any other service that kind of check for new mails even after the application is closed. I think outlook has this feature where it checks for new mails on system startup and does the same even after the app is closed. I guess adding a feature of minimizing the app to system tray would do the job but it will be using way too much resources.
Link to the outlook app I am referring to #https://www.microsoft.com/en-us/microsoft-365/outlook/outlook-for-windows