Got an answer from odoo support:

Hello,

The behavior described in this ticket is known and an internal task to modify it has been created. Although the change may happen in a future version of Odoo.

Note that the conditions for a user to see a project in the Awesome Timesheet App are: Project must be active and at least one of the three following conditions is true:

- the user is assigned to at least one task of the project

- the user has already done at least one timesheet in one task for the project

- the user is set as project manager for this project

also the project must be in the user's favorites

I hope this helps

Best regards,

Lucas