Lee_52 --
On Windows 10 doing Windows key+R, %LocalAppData%Packages\Microsoft.MicrosoftStickyNotes_8wekyb3d8bbwe\LocalState - brings me to the file location of the plum.sqlite files.
However, doing that same procedure on a Windows 11 laptop does not yield anything.
I tried the same thing and got the same result you did -- nothing.
I found it manually, so it's there: C:\Users\YOURUSERNAME\AppData\Local\Packages\Microsoft.MicrosoftStickyNotes_8wekyb3d8bbwe\LocalState
I tried, as you did, to copy the plum.sqlite, then tried copying all the plum.sqlite files. Nothing.
Just for the heck of it, I copied everything that was in the "Microsoft.MicrosoftStickyNotes_8wekyb3d8bbwe\LocalState" folder to the new location (new LocalState folder) -- AND IT WORKED! I have all my notes back!
Fingers crossed it will solve your problem, too. Good luck!