I don't know if I'm in the right place here.
I have the LibreElec 11.0.6 image running on my Raspberry Pi 5.
Unfortunately I can't get a browser installed.
For example, how can I install google-chrome-stable-122.0.6261.111-1_amd64.deb via the terminal (ssh)?
amd64 is 64bit intel/amd architecture. Not 64bit ARM.
You expect to install software compiled for different architecture and for different operating system.
Generic Libreelec builds are not set to run graphical browsers since they started using same setup in v11 for all their archs. Kodi is available as package in Debian and Ubuntu ARM builds. Just run full OS and add Kodi from their package repos.
Even if NordVPN have arm version, they probably don't expect to be run on appliance level OS.