It appears that I can add a group to a Google Developers Console project.
Project owners can share a project with an email address that represents a group, but every project must have at least one project member that is an individual, not a group.
To add a team member or group, select Add Member. You must provide an email address that is associated with a Google account. If the email address belongs to an individual, an invitation flow is triggered, and the new project member must accept the invitation before they can access the project. If the email address belongs to a group, the group is added right away, with no invitation step.
However, when I add a group, the project does not appear for members of the that group, and when they go to the URL, they see
Error The project you requested is unavailable.
Is the documentation out-of-date, is there a bug, or am I missing something?