Does anyone know of a window manager or some sort of "app tray" that allows me to press something like the super key plus a number to choose the app I want but press it again to start cycling through the apps in that "number column"? I'll try to clarify better if my description is a bit confusing. It doesn't necessarily have to have your typical looking app tray. Could even be those interesting circles too.

Do you mean that as in, having 10 applications bound to 0-9, and being able to cycle through instances of that application by repeatedly pressing the corresponding number in the number row?

Basically, but it'd be different applications in one number slot rather than cycling through one application's instances.

You could probably do it pretty easily in Hyprland with the monocle layout and making SUPER+[current_workspace_nr] switch to the next application by adding some lua to your keybinds.