The original hose does have a non-braided (smooth rubber) sleeve on it just down (to the right in my pictures) from the break point. But your codes appear to be "too rich" codes, which is probably a different problem from a crack or break in this hose. My hose break gave "too lean" codes.
From looking at your codes (see below), the P0455 may be the most important. It could be an open or poorly-sealing gas cap, as an easy first thing to try to check. I would do some searches for P0455 and get some ideas to check out. Good luck.
From the Bentley manual (for M54 engine):
P0172 - System too rich (Bank 1)
P0175 - System too rich (Bank 2)
P0313 - Misfire detected with Low Fuel
P0455 - Evaporative Emission System Leak Detected (large leak)