I just tried Ubuntu Budgie 18.04.3 and while it does use entire primary
display on the lock screen, it struggles to use the secondary display at
all while a live system. I would install it next to my Xubuntu
installation and give it a shot to see if I could get I could get it
working properly but
You filed this bug report under "budgie-artwork" - budgie uses gnome-
screensaver, so I've changed the package for the bug-report.
Note though - your bug report also states that your current desktop is
"XFCE" - so what are you using?
I would recommend that you test this on a clean live session
