Welcome! This forum has a treasure trove of great info – Scouters helping Scouters! Just a heads up, though - all content, information, and opinions shared on this forum are those of the author, not the BSA.
In Scoutbook, to connect a scout to a MBC, you first have to “start” the MB for the scout by going to the scout’s advancement page and “adding” the MB if it isn’t already listed by clicking the “Start a merit badge” button.
Have all of the scouts you’re trying to add already had that step completed?
I did not realize that. Opening the merit badge also provides a shortcut to invite the MBC at the same time which was the solution to my original question.