Yeah, I noticed. You can hover on it, or click it to make it permanent, so that it doesn't disappear when you hover out. TBH hover for discoverability on a menu also feels weird.
In the old UI, there was a size mismatch between the status indicator and the ellipsis button. You could be easily thrown off by that, expecting the ellipsis button to have the same area, and ending up opening the conversation instead, because the clickable area was smaller and you clicked outside it. Here it's pretty much the same problem: you end up opening the conversation by mistake, because the clickable area of the ellipsis button is not what one expects. But even when just hovering (though I think most users will still click on it), having the hover work only from one side, because the ellipsis is not centered, also feels weird.