Have you compared these results with what X11 gives you? (I know Windows is not X11 but you can have a simple X11 server by using something like MobaXterm on Windows).

use strict;
use warnings;

eval {
    use X11::Protocol;

    # Screen dimensions
    my $x11 = X11::Protocol->new ();
    my $screen = ($ENV{DISPLAY}//":0.0") =~ m/\.(\d+)$/ ? $1 : 0;
    $x11->choose_screen ($screen); # Root window
    printf "Screen is %4d x %4d x %2d pixels (%3d x %3d mm) (X11)\n",
        $x11->{width_in_pixels}, $x11->{height_in_pixels}, $x11->{root
+_depth},
        $x11->{width_in_millimeters}, $x11->{height_in_millimeters};
    };

eval {
    use Tk;
    my $mw = Tk::MainWindow->new;

    printf "Screen is %4d x %4d x %2d pixels (%3d x %3d mm) (Tk)\n",
        $mw->screenwidth, $mw->screenheight, $mw->depth,
        $mw->screenmmwidth, $mw->screenmmheight;
    };
[download]

$ screen_size
Screen is 3840 x 1200 x 24 pixels (1014 x 317 mm) (X11)
Screen is 3840 x 1200 x 24 pixels (1014 x 317 mm) (Tk)
[download]