The equivalent of “purge” in Pacman would be pacman -Rn (remove a package and it’s configuration files), or pacman -Rns (remove dependencies as well–use with caution). This may be a useful reference to bookmark: pacman/Rosetta - ArchWiki
In either case, config files stored in the user’s home folder should be deleted manually because Pacman typically doesn’t mess with those.
rm -rf ~/.config/vivaldi