Could the hamburglar menu render the popup more central rather to the left of the window, and dim/blur the bg content since it's where users are dealing with their settings tab etc?
Also I only tried in a couple of mobile browsers but the "i" icon to the left of the Lemmy version doesn't do anything?
In regards to the clicking of the Lemmy version and the info button I reckon there could be a nice flow there.
Have it give up options for the state of the current instance, and then link maybes to a wiki / static page hosted by some awesome peeps like yourself with more info / federation info etc?
Currently it doesn't do nuffin and makes mobile lad sad :(