Rekha Sharma who plays Avi was a regular from Battlestar Gallactica and also starred in a few episodes as Commander Landry of Star Trek Discovery (What's Past is Prologue, The Butcher's Knife Cares Not for the Lamb's Cry, Context is for Kings )
In the alternate Captain Kirk's "Ship's Log", he states he has been on the "Defiant" for 31 years and searched 27 parsecs of space.
When Kirk grabs and holds alternate Kirk up by hugging him, it is very reminscient of the scene in the Star Trek: The Original Series episode "The Enemy Within" wherein good Kirk grabs and compassionately holds evil Kirk (both played by William Shatner).