first, thanks to @Denis_Pollini who noticed this little bug in DokuWiki.
When you set internal authentication and the admin user isn’t named admin or administrator then she has no admin permissions after login.
If a domain non-admin user is just named admin/administrator he may get full admin permissions in dokuwiki.
My proposal to solve the bug is
using @admin so any internal auth admin should get the right permissions (as he is in the internal admin group)
using @domain\ admins group instead of user names, this way any domain admin is dokuwiki admin