Just looking at that dropout and the bolt to hanger arrangement, I think you’ll be fine. That bit you’ve split just looks like an aesthetic bit to be honest. You might almost refer to it as a ‘flange’ (chuckle).
Initially I thought it might be important butting up to the step in the hanger, but as there are two bolts, I don’t think this is the case.
If you want to know about steel and mech hangers and how resilient they are check out this thread:
Bent mech hanger on a steel frame?
On my frame the hanger is an integral part of the dropout. It was about half as badly mangled as peterpoddys (see blue frame pics near bottom of thread).
All that was required to fix mine was a large adjustable spanner, a bit of careful pulling and a prayer or two.
It now runs absolutely fine, although I have changed to 1×10 with a clutch mech and a narrow-wide chainring to reduce dropped chain foul-ups in future.
You will be fine with yours I am sure.
Good luck.