Even in TOS, McCoy and M'Benga's surgeon tunics didn't have rank insignia, neither did Nurse Chapel's uniform, or the formal uniforms (although some braiding along the front was used to distinguish senior and flag officers, IIRC).
The actual rank was denoted by the braid. Note the differences between Captain Kirk [wide collar/main seam braid & shoulder seam piping], Commander Spock [wide collar/main seam braid only] and Lieutenant Commander McCoy [collar/main seam piping only]dress uniforms:
Commodore Mendez wore the same dress uniform as Captain Kirk in "Menagerie", evidently, there was no difference for flag officers?:
Hope this helps.