You got a few choises.
Based on what can be seen on the pics it looks like a impact damage, not a fatigue break. The hub may hide some invisible cracks somewhere.
I don't think that area is subjected to a overly lot of tension or a ovely lot of varied strain, but because both sides of the flange are machined, there is no room to leave any weld material except precisely the thickness of the existing material.
Of course it can be welded, turned, machined or ground back to very close to original. That takes some expert welding to build up a new bit of flange with a flawless weld remaining. On top of that there is holes to be drilled right in the weld for the spokes.
The bits could be brazed, but that isn't restoring the full strength.
What will happen if a bit of the flange brakes off entirely? The wheel looses stability, the rim becomes warped and a few loose spoke ends starts to flail about.
There is an excellent repro hub readily assembled with a new brake drum to be bought or you can try to find a used one.
I would explore those alternatives first.