@Martin_fr, many thanks for replying!
I hadn't focused explicitely onto the topic DPI / high-DPI / PPI (on old host vs. new host) yet, an area where i'm not so familiar yet; my todo.
But, as my first suspicion had been (somehow depend), 'scaling', i had set for test the scaling from 125% (actual value) to 100 %, without noticeable impact.
As i previously had read some web threads about the dual monitor theory (but, actually i've only the laptop's internal monitor available, screen res. 1920 x 1080; scaling 125

as well as a possible impact of 'remembered previous display configurations' combined with an advice to change, i'd tried, within the Display settings, "Multiple Displays" > "Remember window locations based on monitor connection":
i did uncheck this -> no effect.
If i set, testwise, the screen res to 1280 x 1024 (that was the old monitor's setting, afair) -> no difference.
The SHFileOperationW-driven popup had been in Win10 the same as in Win11, afair. At least they appear to look mostly identical in Win 10 and 11 to my memory.
Besides: i'm aware that meanwhile MS had leaving SHFileOperationW paradigm; but that should not influence the window pos of the previous API-call.
"Mouse position at the time of issuing the command vs getting the popup": for me: in Win 10 somehow bound together - at least the popup stayed within the listview where the click on "Paste" triggered the command. If enough space available of course. In Win 11 completely separated: it looks like the popup does appear, whenever possible, on a same left side position, whereever the app's form and it's listview had been moved to. So, if i move the form more to the right side of the screen (with still having enough space for the popup!), the popup will emigrate out of the form (and the listview anyway), insisting on it's old used position on the left.
The second screenshot does show this separation between form and popup. Very strange and counter-intuitive.
I appears as if behind the scenes some different rules had been applied to let the popup appear on a fixed place, separated to the mouse pos.
About WM_messages not having been responded to / redirected to the form: could be, but hard to answer, as the previous Win10-desktop is no longer available for comparison purposes.
The good news: it's not a Lazarus issue :-)