Why is a user not available to add to a project team?

Before a user can be added to a project team, they must be assigned the Project Resource user type in their User permission set.

Contact your system administrator to have this assigned to your resources.

Related links

Assigning a project team
How do I prevent all users from being automatically assigned to new projects?
Why can't a resource enter time against my project?
Assigning tasks to team members
Setting up a project