Rule of thumb: Projects needed to be published to be visible by non-owners. Sharing files of a non-published project is also not possible.
Many issues related to projects not being visible to users, even though they have been shared, are related to the fact the project hasn't been Published.
It is not stated in the platform that projects should be published to be visible. This is mentioned when the project is unpublished, though:
If the user still can't see particular folders in the project, check their permissions in the Team tab and make sure the correct folders have been shared with the correct permissions: