Bremskraftverstärker oder dessen Schlauch undicht

Vacuum escaping from the brake servo or the hose feeding it, which is an intake leak with a safety dimension. The servo is one of the largest vacuum consumers on the engine, so a failed diaphragm admits a great deal of unmetered air straight into the manifold — and produces lean and idle codes that point nowhere near the brakes.

So the fault is usually found while diagnosing something else. A rough idle, a lean condition, and fuel trims that improve when the servo hose is clamped are the classic sequence. A hard brake pedal, or a pedal that sinks when the engine starts, is the direct symptom and is the one worth asking the driver about explicitly.

Check the hose and its check valve first, because both are cheap and both fail. The hose perishes at its ends and the valve sticks or leaks, either of which mimics a failed servo. Clamp the hose and see whether the idle settles: an idle that recovers locates the leak downstream in the servo, and one that does not moves the search elsewhere. A servo whose diaphragm has failed can also draw brake fluid through from a leaking master cylinder, which is worth looking for when the hose is removed.