Hello Barry,
Thank you for your reply.
You were right, I tried to update the same item I was modifying and I thought that this might be the problem, so I minimized it to the bare bones, to see what would happen.
Looks like that:

Then I modified one item in my list:

And nothing happened (Ignore the old runs. They came when I recreated everything):

I waited for a minute to see if it will trigger delayed, but no.
Then I modified the second item:

And there you go, both runs get triggered. One after the other:

Like I said there is a minute between the modifications of the two items. If I wouldn't modify a second item the first would never trigger. Even though it isn't the same flow I still get the same results, so the problem must be by the trigger event itself.
Then I repeated that several times:

I created a workaround by replacing the edit-dialogue in the list with my own from PowerApps. In my App I started a slightly modified flow in the OnSave event. That's almost the same as when I modifiy a item without replacement.
But this doesn't fix the issue itself.