Today Page on Mac: Move its window independently between desktops

Hi, I’d like to keep the Today Page open throughout the day and bring it to whichever desktop or display I’m currently using. My main GoodTask window should stay on its usual desktop alongside Calendar and Contacts.

Observation
Dragging the Today Page window to another desktop in Mission Control has not worked reliably for me: it stays on the original desktop. I did manage it once, but I haven’t been able to reproduce that.

Confirmed workaround
Holding the window with the mouse while pressing Control + Left/Right Arrow to switch desktops does move it successfully. However, that combination is quite awkward for everyday use.

Requested improvement
Could you provide an easy “Show Today Page on this desktop” action that brings the existing window to my current desktop or display without moving the main GoodTask window? Reliable dragging through Mission Control would also help.

Assigning the entire app to all desktops would not fit this setup, since I want the two windows to behave independently.

I’m not sure what causes the current behavior, but I hope this description helps. Thanks!

Thanks for detail explanation. I'll take a look. Thanks!