As a system administrator, you must update your organization’s Salesforce user profiles to allow access for users who will maintain project tasks.
In Project Task Gantt only resources that are the designated project manager of a project automatically have permissions to read, create, update and delete project tasks. Other resources cannot edit, create, delete or update project tasks unless you grant them Create, Edit, Delete and Modify All permissions on the following objects:
Other resources must have been assigned either the Project Task Gantt View or Project Task Gantt Edit permission control. For more information, see Permission Control Fields.
Ensure the "Bypass Internal FLS and CRUD" security settings are selected if you want to use the Project Task Gantt Edit permission control. For more information, see Security Settings.