After installing pacman packages (last one was 'ungoogled-chromium') my root partition of 20GB is completly full. Now I can't update new packages.
My partition structure is: root (20GB) /home (470GB) swap (10GB)
How can I delete the garbage that is piling up in my root, and how to prevent it from happening again.
Sounds like you don't clean your package cache. You can enable the paccache.timer to handle it for you on a weekly basis.
https://wiki.archlinux.org/title/pacman#Cleaning_the_package_cache