After searching a bit I found the MediaWiki config option $wgSMTP that can be added to LocalSettings.php in the wikibase container.
$wgSMTP = [
'host' => 'mail.example.com', // could also be an IP address. Where the SMTP server is located
'IDHost' => 'example.com', // Generally this will be the domain name of your website (aka mywiki.org)
'port' => 25, // Port to use when connecting to the SMTP server
'auth' => true, // Should we use SMTP authentication (true or false)
'username' => 'my_user_name', // Username to use for SMTP authentication (if being used)
'password' => 'my_password' // Password to use for SMTP authentication (if being used)
];
docker cp wikibase-docker_wikibase_1:/var/www/html/w/LocalSettings.php LocalSettings.php
edit LocalSettings.php
docker cp LocalSettings.php wikibase-docker_wikibase_1:/var/www/html/w/LocalSettings.php