Is it possible to make admin toolbar partially visible to newly created users in Drupal 8? For example, the user would be able to observe the Reports, but not be able to add new modules, so the 'Extend' entry is not visible to him?
Yes, as Neo mentioned, the toolbar utilizes menu permissions so it only displays items available to the user. So if the user has permissions for Use the administration toolbar & View site reports (or whatever permission needed for a sub-item in the admin menu), they will see only the report menu items.