Your laptop is definitely recognizing the eDP display as having a 165hz setting at 1080p.
I am not familiar with KDE, but you should have a displays section in the settings where you can change the resolution and refresh rate. Can you change it there to 165hz?
First, before anything else, it looks like nvidia-lts is indeed in the extra repo. Try refreshing the repositories with this command:
‘sudo pacman -Sy nvidia-lts’
If this solves your problem as you mentioned, no need to proceed any further. If this is still unavailable, it may be one of the dependencies which is solving your issue so try installing those.
sudo pacman -Sy libglvnd nvidia-utils nvidia-dkms
There is also linux-lts and linux-lts-headers, but you are not currently on an LTS kernel. (This may be why it is unavailable?)
Now try change your resolution in the system settings or with nvidia-settings if you can.
If it still doesn’t work
Update your driver with the following command and try changing resolutions.
sudo mhwd -a pci nonfree 0300
Here is someone using xrandr to view supported displays and refresh rates that may be helpful in troubleshooting further:
There is also the Arch NVIDIA wiki page that can be of help.
It is of note that there can be issues when having multiple monitors at different refresh rates. Try disconnecting the second monitor you have attached to the hdmi port and try changing refresh rates.
If you are still stuck, post the output from xrandr