It will be the same issue - both budgie desktop and gnome-shell share the same window manager called mutter.
So - for whatever reason - gnome-screensaver is probably recognising a different resolution when locked compared to when unlocked. When the unlock occurs that lower resolution is retained by the window manager.
So the issue probably still is in the gnome-screensaver code.
As to a solution - I don’t know I’m afraid. One of these days I must get a super high resolution monitor to see if I can reproduce what some people like yourself are seeing.
Do try connecting to your monitor in a different way - e.g. VGA/HDMI to see if its the connection choice that is invoking your issue.