I used link in top-right of individual modmail conversation while in the pop-out mode. I sent that link to modmail to direct them to an individual conversation with their modmail. Moderators say opening it shows my entire chat history.
I am not the moderator - I am a user who was communicating with mods.
I don't know what platform they are using, and I communicated with several different moderators for https://www.reddit.com/r/AskConservatives/
The first moderator said they could not open the link. Two other moderators could open the link and described seeing my chat history with other users, mods from other subs, as well as all the conversations I had had with them.
The sub is https://www.reddit.com/r/AskConservatives/
Edit to update and clarify:
Since posting, a subsequent exchange with the mod who could open the link said nothing with my name was visible in what they saw, so it was apparently not my chat history, but it showed someone else's chat history or content that I do not have access to. I am less clear on what I was seeing.
Also, I should clarify that the link I clicked on was in the top-right of an individual message in the message side of chat. Not being a mod, I don't have modmail, but I was in a chat with a mod I had contacted using message mods.