38:02 I don’t see how this is a big deal, that Gideon was taken by Mandalorians. They are scattered around doing mercenary work. Din Djarin was working for him in the first episode, through his lackeys, Dr Pershing and Werner Herzog. Only an idiot, or a character written by the creative team at Disney+, would assume this has anything to do with Din Djarin or the covert, much less act on that notion. Also, Gideon’s people paid Din in refined beskar, and Gideon himself carried a singular Mandalorian weapon. That he has allies or retainers with access to Mandalorian tech or materials should not remotely be a dramatic reveal.
Seems possible that the dark troopers from the last couple of episodes of Season 2 have beskar-alloy armor (but not likely pure beskar). Could be a piece of a dark trooper that boarded the shuttle to rescue Gideon.
"Blue Boy" confused me too. Wookiepedia has this, which I thought was a possiblilty:
So maybe the New Republic is using blue-shooting blasters? I don't remember...