Hahaha. Common problem with multiscreen with different resolutions. Your laptop screen is below and left of your main display, and X11 renders this black "virtual screen".
There are multiple solutions:
a) Set your screen resolution and position through KDE Plasma SystemSettings and push the button "apply to SDDM configuration" (I think Plasma 6.0 removed this option, try to find it in the SystemSettings KCM SDDM section).
b) The another solution is the old one. Create a file into /etc/X11/xorg.conf/display.conf with the proper values of position and resolution. Search in a wiki about examples (archlinux wiki?).
c) There is a third one that I used few years ago. SDDM allows you run any command after the screen initialization. So you can exec your xrand command here. Search about /etc/sddm.conf
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