How do you change the output bag type with the recycler?

It's both sides, it's a config option. Whatever modpack is claiming the bag ID for Loot Recycler output can be changed in game either has a typo or using a custom addon I have no knowledge of or control over.
Unless you are mistaking the Loot Recycler (green block) with the Bag Storage Block (red block), then there is a GUI button the change which bag the storage block outputs.

The IDs are listed in the lootbags_BagConfig.cfg file, each bag starts with
$STARTBAG:lootbag_Common:0
that number at the end is the ID.

I've changed the value in the cfg both server and client side to 4 (epic) and the bags in the recycler are still "common"

Did you restart the server and clients?

yes I had, it was dumb, the first bag in the queue was still common, after that, legendary. Thanks!

In the lootbags.cfg file there is a field called
I:"Bag ID used in Recycler"=0
change that number to the ID of the bag you want.

Is this server side or client side? Description of modpack says there's supposed to be a GUI button to change the bag type?

What is the ID of each bag type?