SQL-Server login-error of SQL-Server Agent Account
The user account that is running the SQL Server agent might not have permissions to use the database mail profile you can check that with EXECUTE msdb.dbo.sysmail_help_profileaccount_sp;

But you are having some issues with the agent account security, please try the following steps.


Remove all extra privileges from the Agent user account (or create a new domain account) Running the SQL Server agent with domain admin privs is just terrifying.
Change the user for the Agent service using the SQL Server Configuration Manager. You should never change it any other way as it will set all the necessary permissions. Change the account to network service and then back again and make sure beforehand that the agent user is neither a local or domain administrator.
Check the mail profile on the SQLAgent settings and make sure that it's not private and that the agent user account can use it (The user account will be made sysadmin by the Configuration manager and should be able to use all accounts)