A4 B7 Throwing Code for Lean in Bank #1

2005 A4 B7 2.0 T

Car is running rough and it seems break boost assist is lacking in power...The car has little break pressure initially when started and only after driving does it seem to work correctly. After I was probing thru hood I noticed a hose coming off the break booster assist went to some "Valve" that seemed to have a little up and down play. I took a photo of area in question with hose removed from "loose" fitting.

What exactly is this fitting?
Can it in any way be the "lean causing issue"
How do you replace it?

Please get back with ideas