we got the problem solved by changing the port number from 587 to 465.
Now we are also able to send E-Mails to Amazon WorkMail / SES using APEX_MAIL package.
Why it makes a difference we cannot explain yet, as the APEX_MAIL package is built upon the UTL_SMTP package according to Oracle documentation.
Our working settings now are:
SMTP Host Address: email-smtp.eu-west-1.amazonaws.com
SMTP Host Port: 465
SMTP Authentication Username: UserName
SMTP Authentication Password: Pw
Use SSL/TLS: Yes
Default Email From Address: firstname.lastname@example.org
Maximum Emails per Workspace: 1000