I generally use a quick flick of the mouse to switch focus between windows on different monitors. I generally keep the same application on a particular monitor so know where it 'lives'. I usually use the Keyboard Alt+Tab to cycle between windows that are covered by others, so from that POV it's quite confusing when Alt+Tab causes windows on the other monitor to the one I'm looking at get cycled.
Is there any way to limit the list of Alt+Tab windows only to the current monitor that has focus?
I'm on GNOME, not Compiz, on Ubuntu 19.04
Short answer
This snippet was written on request for Ubuntu Budgie, but should work on anything but Wayland. It switches between windows on current workspace & monitor, and, depending on the possible argument, either between all windows or between windows of the active application.
It doesn't show any animations though, it just cycles through windows.
Setup instructions are in the link.
Disclaimer: I am the author
You can use either the Current screen only on window switcher extension or the Alt-Tab for Dual Monitor extension. They both work similarly and cycle windows on the current monitor (the one with the mouse) only.
Although it is mentioned in the GNOME Shell extensions webpage that they support GNOME Shell versions up to 3.32, they both work fine for versions at least up to 3.36 (that's what I've tested).
Also see this question for how to install GNOME Shell extensions: How do I install and manage GNOME Shell extensions?