The hose that broke is actually a vent hose that connects from the air filter housing breather hose to the fuel pressure regulator (2nd photo with blue line).

If the diaphragm in the fuel pressure regulator (FPR) fails, fuel will vent thru' this hose from the FPR to the breather hose.

It's not a vacuum hose.

I have seen this hose broken off/disconnected in quite a number of MBs with no problems.

Cheers.