Amethyst
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How to define which display is "screen 1" and which "screen 2"
Using Amethyst v0.15.4 (91) on MacOS Big Sur, and working with an external monitor.
With most external monitors, throwing windows (⇧⌃⌥ + 1/2) to "Screen 1" → internal macbook screen and to "Screen 2" → external monitor. But with some other external monitors (office with flexible workspaces), these are switched: "Screen 1" → external monitor and "Screen 2" → internal macbook screen.
Is there some way I can define/change these screen settings, and set "Screen 1" to always default to my internal screen? I already tried dragging the menu bar in the Display : Arrangement preferences, but that didn't work.
I think it hooks into macOS's Display Preferences. I think this is also the case for setting the "main" screen. I was able to change the main screen by going to System Preferences -> Displays -> Arrangement and then drag-and-dropping the "title bar" from one display to another. The display with the title bar seems to be the "main" display with meta+M.
Because of this observation, I think Amethyst is determining which display is "Screen 1" (or "Screen 2", etc) from the system's display index. I only have one external display, so I cannot confirm my hypothesis. If my hypothesis is correct, then perhaps unplugging the displays, and reconnecting them in the correct order (or finding a way to programmatically re-index the displays at the OS-level) might help you.
If you find the solution, please share it because I am sure others are curious too.

I have the same question.
I use iPad sidecar:

And internal macbook screen is "monitor 1":

but when I use Amethyst shortcut "throw focused window to screen 1", window on internal macbook screen will be moved to iPad sidecar screen. When I use "throw focused window to screen 2", window on iPad sidecar screen will be moved to internal macbook screen.
Monterey 12.3 Beta (21E5227a)
Screens are sorted horizontally on the x-axis. The actual labels are uuids and do not lend themselves well to shortcuts.