In order to see the public collections of any user, you go to https://musicbrainz.org/ws/2/collection?editor=username

In order to see all collections (including the private collections) of of any user which you can log in as, you go to https://musicbrainz.org/ws/2/collection?editor=username&inc=user-collections

That's quite confusing, since both of them show user collections. The second has private collections included, so the obvious inc parameter should be called private-collections :​)