I have this question too, and while I've not yet found a way to tell exactly who enrolled a user, I found that the user/enrollments API report has a column titled "sis_import_id". It appears that may be related to the specific import event that enrolled the user (so I inferred that if that cell was blank for a given row, then the user was enrolled manually via the UI). If that is indeed the case, when there is a value listed I think I could look up the import event for that value to see which user initiated it. I've not had much time to dig into that aspect, and it still would not tell me what user made a specific enrollment via the UI but it could be a start for some type of discovery. Again, thanks for posting this question!
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