I know in Settings > Taskbar > Taskbar Mode
I can set all or nothing for the taskbar on whether I want windows to be displayed on the relevant taskbar, or all taskbars. I'd like to see a compatibility setting option where I can single out a specific application to be seen across all monitors. Conversely a setting to show an application on only the relevant monitor.

I've asked to show the window on all monitors, but that's just a workaround. I'd really like to be able to pin the application to a specific monitor taskbar even when minimized. (Regular pinning shows the icon even when the app isn't running, but when the app is running on a different monitor the pinned item would just launch another instace.)

Usage scenario: I have two different RDP shortcuts setup for the same client. One uses a single monitor, the other uses all monitors. For the one that uses all monitors when minimized it only displays on Monitor 1, but I'd prefer it show on Monitor 2.