What proved to work in our case was altering SMTP settings by directly updating SonarQube's database.

First I changed the SMTP configuration on the GUI, supplying dummy credentials for authentication. Obviously, these credentials did not work, but this allowed me to change the other SMTP-related fields.

Database connectivity settings can be found in conf/sonarqube.properties - look for property keys starting with "sonar.jdbc", such as sonar.jdbc.username, sonar.jdbc.password and sonar.jdbc.url.

What to look for in the database:

-- email-related properties
SELECT * FROM internal_properties WHERE kee LIKE 'email.%';

-- erasing credentials (2 rows)
UPDATE internal_properties SET is_empty = true, text_value = NULL WHERE kee LIKE 'email.smtp_________.secured'; 

After the DB update, I restarted the SonarQube instance. From that point, email notifications started working again (I sent a test email from the web GUI).

This is something you should do with caution. Also do a backup and have a sound plan on how to restore it if something bad happens.