This is a message from you, Chris, in 2018, on GMF (emphasis added).
Title: "Possible Missing Activity"
And here are a few more. Easy to find: just search on the ubiquitously suggested workaround, "bcc":
"I don't see a record of these direct emails under Admin->Activity.
"These don't show up in Activity for some reason, which maybe is a good suggestion for Beta"
"When using the "Send message" function to email a member about a pending post, is the message saved somewhere? I have looked but can't find them."
And on and on they go, back to the beginnings of time. It has almost become a hazing ritual for new members! They need to be put in their place, informed that the messags are not logged and and told to "just use bcc"!
I didn't bother to search beta but the request has been ongoing here, as well. I know because I've participated in them. (I'm not in GMF but I was sure new people had to be wondering why these messages were not logged, so I searched there. I was not wrong.)
Messages are the sole opinion of the author, especially the fishy ones.