The first time “Barry” used such a background gag was its second-ever episode, “Chapter Two: Use It.” Barry visits his handler Fuches (Stephen Root) at his hotel and then takes a call from Sally Reed (Sarah Goldberg). As Barry is talking on the deck, armed men burst into Fuches’ room and attack him. Fuches fails at trying to fight back and get the oblivious Barry’s attention.
The framing of this scene is different than in “you’re charming.” In “Use It,” Barry is on the right edge of a frame taken up by a paneled door. This leaves plenty of space for us to look in at the action unfolding with Fuches. The camera even goes to a wider shot once the door gets busted in; our focus goes from just Barry to two things happening simultaneously.
Another gag of this sort is in season 3, episode 2, “limonada.” Gene is trying to flee Barry and winds up running through backyards in suburban LA. He stumbles into one that has a whole pack of dogs waiting for him. The inhabitants of the house are having dinner; one is leaving the other because she has “too many dogs.” As she says this, we see at least two dozen dogs run past the window toward Gene.
All three of these episodes were directed by Bill Hader himself, so it’s safe to say these moments are part of his artistic thumbprint. Hader was already a renowned comedian and actor, but “Barry” let him prove his chops as a filmmaker. “Characters in the foreground oblivious to the background” is cinematic comedy at its best.
Source : https://www.slashfilm.com/1265997/barry-season-4-episode-3-funniest-scene-continnues-key-series-trend/