As a Team Member, you will have access to all non-private Projects on the Team.
However, you must be added to the project to receive notifications.
Click the (+) plus sign at the top right of the project and select Add Your Team (the name of your team will be shown). You'll then have the option to add any Team Members not already added as users to that project.
To add one Team Member to a project click the (+) plus sign at the top right of the project and select Add Individual all Team Members from your Team who are not already added to the project will be shown 👍