Notifications

Use an internal relay that wants no password

Plenty of organizations run a relay that accepts mail from known hosts by address and has no accounts at all. A tool that insists on a username and password cannot talk to it.

What to do

Open Notifications and choose SMTP as the mail method.
Enter the relay host and port. Port 25 with no encryption is normal inside a network; 587 with STARTTLS if the relay offers it.
Leave the username and password empty. Both are optional and the product will not add authentication that was not asked for.
Set the from address to something that will survive a person leaving.
Press Send a test.

A tip

If the relay refuses, it is almost always the source address rather than the mail. The host running the container is what needs to be on the allow list, and inside Docker that may not be the address you expect.