I believe this is no longer a problem with the main ISOs, but first I would check if your user is in the sys group. If not, I added my username mparillo (substitute your username) with:
$ sudo gpasswd -a mparillo sys
Second, when you installed hplip, I would check to see which optional dependencies were installed. For example:
Optional dependencies for hplip
cups: for printing support
sane: for scanner support [installed]
xsane: sane scanner frontend
python-pillow: for commandline scanning support
python-reportlab: for pdf output in hp-scan
rpcbind: for network support
python-pyqt5: for running GUI and hp-toolbox
libusb: for advanced usb support [installed]
wget: for network support [installed]
So, I installed:
$ sudo pacman -S python-pyqt5
$ sudo pacman -S cups
Then, since you are on KDE, I would check for system settings controls (generally present except on minimal installs), but if not installed:
$ sudo pacman -S print-manager
$ sudo pacman -S system-config-printer
Last, I would enable CUPS if not already enabled before starting HP Setup from the command line:
$ systemctl enable org.cups.cupsd.service
$ systemctl start org.cups.cupsd.service
$ hp-setup -u