See the privacy setting has changed in that there’s no “overall” setting for a record. Do I have to do each fact/event?
If so, what would be the purpose of setting via Administration vs each fact/event?
No, the privacy setting for a complete record (whether INDI, FAM, SOUR, NOTE, or OBJE) has not been removed.
What might have fooled you is that they are all selected through a single “autocomplete” field.

(Note: by the way, the word “Adoption” in green on that section is a translation error. Not sure how many languages show it. It should be “Action”. It will be fixed next release).