Would it be possible to make it so Loaders transfer from a belt to a container? without having to install a different mod

it's already the case ? What's the issue ?
With a bit more explanation: the loaders only "redesign" the default loaders from the game which already do belt -> containers and the opposite, so I'm a bit lost with your request

At the moment they take items from containers and transfer them to belts. but not the other way around. Example:

Container > Loader > Belt Works
Belt > Loader > Container Does not work

https://imgur.com/a/OpOY25i

you need to put the loader in the right orientation (the part with the belt in the opposite to the chest, like your top example)
then if the loader is not direction, just rotate it with R (it's the "arrows" on the top of the loader that show the direction)

I see, Thanks. a bit weird but it works nonetheless!