Mail stuck in ExternalMailQueue
This login ([NT SERVICE\MSSQLSERVER ) is needed, no matter DB mail was configured under which service account.
The original SQL service account is NT Service\MSSQLSERVER
Configure Database mail under SQL service account - NT Service\MSSQLSERVER
Next, change the service account to another AD account + drop login [NT SERVICE\MSSQLSERVER]
DROP LOGIN [NT SERVICE\MSSQLSERVER]
GO
Then the issue is reproduced :
Mail stuck in ExternalMailQueue
Don't see "Database process is started " and no additional errors in sysmail_log / sysmail_event_log
But, in Application event we do see the permission denied error
Database Engine Instance=SQL1;Mail PID=1048;Error Message:The update to the database failed. Reason: The EXECUTE permission was denied on the object 'sysmail_logmailevent_sp', database 'msdb', schema 'dbo'.
After re-creating the SQL login, the DB mail function works!
CREATE LOGIN [NT SERVICE\MSSQLSERVER] FROM WINDOWS WITH DEFAULT_DATABASE=[master], DEFAULT_LANGUAGE=[us_english]
GO
ALTER SERVER ROLE [sysadmin] ADD MEMBER [NT SERVICE\MSSQLSERVER]
GO