Proper Terminal Command To Clear Update Cache?

To remove all the cached packages that are not currently installed, and the unused sync database, execute (as sudo) Note the warning about doing this in the wiki.

 pacman -Sc

https://wiki.archlinux.org/title/pacman#Cleaning_the_package_cache

And have a look here for clearing the pamac (Add/Remove Software) cache:

https://wiki.manjaro.org/index.php/Pamac#Cleaning_the_Cache