Can you please try without checking any option ?
Do you have the same message ?

Yes, same message

Do you have some restriction of type of project per profile ?
Possible this profile cannot create projects of the selected type.

No, I'm able to create projects of this type but not to copy them.

Which version of ProjeQtOR are you using ?

V9.5.3

I think you changed some habilitations for the project leader profile (possibly you just changes access modes)
It's difficult to analyse this through forum.

You can tests that default configuration works fine for copy of templates on Demo : https://demo.projeqtor.org
Connect as Manager (he is a Project Leader).
Go to screen project, apply filter for type "Template" : you see all templates in the DB.
Select any template project : you may not be able to change data of the template, but you can copy it into new projets.
Copy Works.

Within the ProjeQtOr demo my proceeding works. Unfortunately I'm not able to compare the access rights because they are not visible within ProjeQtOr demo...

here is a capture of the access modes as they are by default in ProjeQtOr so that you can compare

They are the same within my configuration

Sorry, double post

You may try to install new instance (for instance on your laptop) to be able to compare defaut "standard" configuration (that is used on demo)

I found out: Obviously you need the right "Manager+" to be able to copy a project. Actually, I don't want to give this right to the project leaders, because than they can see AND EDIT all projects and not only their own...

Same for milestones (and possibly all other types of objects) within copied projects: you have to on right Manager+ to copy them

No, for sure, you don't nee "manager +" right to copy a project.
Default access rights allow project leader to copy any template.
You may try on demo.