The Pro Report is scheduled for daily sending, only it does something strange.
It does not send on the time set, but it only sends directly after I open the Pro Reports add-on.
So in my opinion it is not some problem with SMTP, correct?
Any advice?
All scheduled tasks including scheduled emails depend on the core feature of WordPress, WP-Cron, to work.
However, if there is no network activity on the website, such as you logging into the Dashboard site, WP-Cron will not trigger, and the cron jobs will not run.
If you want to make sure that WP-Cron jobs are regularly triggered on your MainWP Dashboard, you can add your Dashboard site as a monitor to an uptime service such as Uptime Robot.
The Uptime Robot will ping your dashboard site regularly and make sure that all scheduled events are occurring.