The access rights work the SAME in both Classic and Modern UI.
The access rights for booking resources and roles must be granted separately from a user that is simply a Project Manager.
When the user becomes the Project Manager, they have edit management rights on the project, but to add staff, they need the additional access to the resources and roles.
Typically customers will create an OBS enabled for use with access rights and create a 'Group' that grants access to 'Resource - Soft Book' for any resources that belong to a specific OBS unit or unit & descendants.
And don't forget to grant 'Resource - Soft Book' access to Roles for adding them to the projects too.