(See the end of the question for details on versions of things I'm running).

How do I ensure that windows open up below the Gnome Top Bar such that the Top Bar does not obscure the edge of the window?

I discovered this odd behavior when playing with notify-send as follows:

notify-send -u critical xxx $'yyy\nThis is a test'

I am using -u critical to force Gnome (or whatever) to not unmap the notification window to give me time to grab a screenshot using Pscr key. That screenshot is:

Invoking dconf-editor causes it to be mapped underneath (in z-order terms) the Top Bar window, leading to a bad situation like this whereby I cannot even close the window because the icon is obscured to the point where I cannot even click on it using the mouse:

I tried to manually close this window by using the Windows key to get to the icon, but it shows that the icon is not there for the dconf-editor in that view either (why? it is for my other top-level application windows, so what makes this one so special?), so I cannot even close it:

So I have to resort to killing the process from the command line using the kill command.

Perhaps the solution to Hide GNOME top bar in activities would solve, or workaround, this problem, by simply automatically hiding the window, but the answers to that question were inconclusive at the time of this writing (2019-12-13). And also How to enable Hide Top Bar Gnome Extension so that it hides the Top Bar? shows that I ran into difficulty getting that Gnome extension to work.

This seems similar to the old issue impacting Unity at How to adjust window placement in Unity, Ubuntu 14.04 based on overlapping top bar but this is specific to Gnome, so I concluded that question was irrelevant.

I'm using Ubuntu 19.10 running Gnome 3.34.1 (whatever Ubuntu uses by default):

Update 1

This is a dual monitor setup. Details of the setup are in the subsequently filed question: How to enable Hide Top Bar Gnome Extension so that it hides the Top Bar?

Update 2

Here is a screenshot of the Settings/Devices/Displays window showing two NEC 24" monitors.

Update 3

I did the following:

1. Uninstalled all GNOME Shell extensions via Update 7 inside How to enable Hide Top Bar Gnome Extension so that it hides the Top Bar?
2. Uninstalled Ubuntu packages for GNOME shells via commands like sudo apt remove gnome-shell-extension-autohidetopbar
3. Rebooting as seemingly required by my discovery in https://askubuntu.com/a/1196222/340383 (which I still do not agree with should be required).

I now retested the notification above via:

notify-send -u critical xxx $'yyy\nThis is a test' 

And now I see that the notification window is mapped below (in the y direction) the Top Bar on the right monitor which is what I was needing in the first place:

Now, this isn't an answer because it doesn't explain why this is now working. I can speculate that vanadium's answer over on https://askubuntu.com/a/1196304/340383 was actually "spot on" in the sense that it forced me to wipe clean any and all GNOME extensions installed via the the GNOME Shell integration Firefox extension as referenced in Update 6 in How to enable Hide Top Bar Gnome Extension so that it hides the Top Bar? (whew!).