Where can I find my previous chats

When I hover over the upper right corner plus and the time, it doesn't show a description of what will happen if I click on it.

So I clicked plus, and had an empty chat. Okay, fine.

Then, I search for my old chat, obviously.

So, looking for it, I clicked on the watch, had the option between 2 chats. But now, clicking on the "clock" again, my old/first chat doesnt show up anymore. So everything I've discussed with him is gone? Or I am not sure where I can find it...:( All I am left with is "the structure" in the middle.