I’m the owner of our company team account and would like to create folders inside our collections. The web interface of the vault does not have that option when clicking “New”. The menu only shows “Item” and “Collection”:
Collections are for orgs, and folders are for individual vaults. You can’t create a folder in the org’s vault.
Here are selected passage from the link you referenced:
Folders are structures used to organize your individual vault
There are similarities between folders and collections. Folders organize your individual vault (but can include shared items) and are unique to you, where collections are shared between members of organizations.
So, you create collections with items to be shared in the org. And the individual user put the items, including those from the orgs’ vaults, into any folder they like.