Do I really need this circuit vent if the sink vertical drain segment is 4' away from the vertical dry vent?
If the slope of the drain is 1/4&quot;-per-foot you can do without the pink vent.  Be sure to measure your slope with a level.  Don't just measure from the floor.
You don't need an AAV to delete the pink vent.
trap arm size    trap max developed length @ 1/4&quot;-per-foot slope
1 1/4&quot;           5 feet
1 1/2&quot;           6 feet
2&quot;               8 feet

Instead of the green branch drain having a vertical drop, just run it horizontally (with a 1/4&quot;-per-foot slope) over to the corner.  That is within the max length before siphoning could occur.