Further data points here on Windows 11…
Setting the shortcut (actually located on my roaming profile) to minimized also made dt start maximized on the external (primary) monitor. But only if I launched it directly from that shortcut in Windows Explorer. That shortcut was also pinned to the taskbar, which is where I was starting it – and from there it starts on the wrong monitor.
So I un-pinned and re-pinned it. Now from the taskbar, it launches on the proper monitor, maximized …with its underlying shortcut set to run minimized. Go figure – gotta love Windows… Sure wish MS hadn’t removed Quick Launch from Windows 11.
I’ll keep all this in mind when it (or some other app) mysteriously starts launching on the wrong monitor again ('cause you know it’ll happen). 