I’ve received several emails from other users in recent days, each with a link “Visit Topic to respond”. Some of these links are blocked, generating warnings from my ad blocker that the link goes through a tracking site, awstrack.me. If I ignore the warning and proceed, it takes me to the topic, but the other senders message is not a part of the thread, so a response in-topic would be inappropriate and I am uncertain that the emails are legitimate, so I have not responded. There are no new messages in my profile, so even if I sent a reply via PM, I would not have the complete conversation saved in Messages.
This is quite different from private messages I have received here in the past. I was notified of those by email, but the link took me to the private message(without tracking), not to a thread. Looking at other user’s profiles, I do not see an option to send an email, only a message, so I do not know why these appear only in my email. Looking at the settings in my own profile, I don’t see anything I can change that would be related to this behavior except possibly to turn off emails notifying me that I have been sent a personal message. I would really prefer to keep emailed notifications so that I can provide prompt responses, but I also expect the entire private conversation to be available in my Messages profile.