That is very, very strange. In default Moodle you should be seeing the Manual enrolment section right between Publish as LTI
Tool and Course Meta link.
Can you check to see which other roles have this? There is a report for this. If you go to Site admin > Users > Permissions > Capability overview, you can run this report. See the attachment for the settings to put in, but basically you want to put the capability enrol/manual:enrol in the filter box for Capability, then for Roles, select All, then click the Get overview button. You should see the results like in my screenshot: where Manager and Teacher have this allowed and for all other roles this is Not set.
That will tell us if there are any conflicts. Are there any other roles that have this set and are there any permissions other than Allow.
Secondly, back in that course. When you look at the Participants page, what roles do you see for the 3 users who are enrolled? Are they enrolled as Teacher, Student, or some other other role?
Finally, you can try to make a new Teacher role and see how that acts. So, in Users> Permissions > Define roles, click the Add a new role button at the bottom, then for the Archtype, choose Teacher. For the shortname, call it editingteacher2. Below that, In the filter area put in "enrol" and check if you see whether or not the whole section called Manual enrolments shows up between the Publish as LTI section and the Course meta link section. You should see that section with five settings in it for enrollment.
Since we know that section is missing from your teacher role, I wonder if it will still be in the default. (Moodle stores a base setting for all the standard roles as the default role. It creates this when you install Moodle. This default never changes, so you can always rebuild any role at any time as reset it back to the default this way.)