I can't speak for the other password managers, but I find Bitwarden's organization management to be pretty terrible. As a personal password manager it's pretty good, but as an organization password manager, not so much.
Apparently there is two different things, Collections and Folders. Folders exist for personal vaults and collections for organizations. No idea why you can't use folders in organizations.
Yeah you're right. I think folders are more like a "tag" in that it's not actually a container (I think you can even put stuff from an Organization's collections in your personal folders).
Anyway, with Collections, you used to have to create a collection and enter the name as Some/Thing, to get a hierarchy going. But I think they improved that so that you can just create that hierarchy of collections int he web gui as if they were folders in folders.