FWIW Qt 6.8 added the property popupType which allows the popup to be opened in a new window, if the platform supports it, which it seems Plasma does.
With qqc2-desktop-style the standard Menu works pretty well. Dialog still draws rounded corners for the main dialog background, which looks odd within the frames of a window border. Kirigami.Dialog still draws a custom title, which is redundant for dialogs that have a title-bar.
So I guess it wouldn’t be too much work to patch Kirigami to disable the custom header for Window popups, and patch qqc2-desktop-style to disable round corners for Window popups, and set popupType: Popup.Window when running in desktop mode. I guess the only issue is that it’s probably too soon for frameworks to depend on Qt 6.8 atm.