The emails sound more like he believes America will rise up spontaneously as a mob to kill both Fauci and his family in terrible ways - and he’s quite happy about that - in a grim, profane sort of way. I don’t see where Connally threatens to do the violence himself. Maybe there are other emails not shown where that happens. Obviously, the sender is mentally disturbed.
From the complaint: “You will wish you were dead when I’m finished bludgeoning your disgusting elf freemason skull into the pavement.”
Sounds like a threat to me.