Hi @Anonymous,
Thanks for the questions and good diagrams to explain your requirment.
What I understood is you want to generalize a flow from a single trigger.
You could try the following

So your trigger going to be Recurrence.
Define your site address.
In the apply each you could add a check condition to check your library name matching "Displayname". I haven't added this if condition in my example. Then check Get Items to get each libraries.
So the next challenge is how the user updated or created a document. So for this you need a custom column to add in your SharePoint document libraries called 'lastcheckedbyflow' with a datetime. Check this by modifed date from the meta data of "Get items". Then do your rest of the logic to send alert. Once the alert is send then you update the list column 'lastcheckedbyflow' by using the same value as modified date. So when next time a user updates the same document the 'lastcheckedbyflow' value is different so that you can send alerts.
If it is useful then please accept this as solution.
Let me know how it goes.
Thanks