Hi and welcome!
Maybe this thread is also interesting for you: Notification not Work - Notification with Pushhover? Because first of all is to understand how the notification are working with icinga. In short: Icinga runs only a script, what the script is doeing doesn’t really matter and icinga don’t know what it is doing - it could send an sms, email, using a messenger service or only write “hello world” to the console. The same with the check scripts! Icinga exepects only a return value and maybe a output.
If the script runs your notification script, you’ll see the message in icingaweb2 as done - like in your hardcopy.
the next thing to know is, the director don’t installs checks - there are no included. With the kickstart functions the director import the checks from the icinga ITL (look here: /usr/share/icinga2/include) . Icinga installs this two notification script in /etc/icinga2/scripts. These are “mail-host-notification.sh” and “mail-service-notification.sh”. We for example don’t use it. We are using our own python script.
What does it mean? Check your notification script if file or security permissions are missing. Check if your shell user- you wrote you are using nagios - has permisisons to run your mail program “msmtp”. If these things are correct, check your firewall logs if there is something strange.
I Hope this helps a little bit