I suggest: Patch it up (I use cloth first aid tape; make sure to cover the wound with something breathable, stretchy and non-toxic, not just tie/wire it together) and it will almost certainly be OK. With the rather clean vertical split, actually little or even negligible damage was likely done to the living tissues in the stem -- the xylem (transport up) and phloem (transport down to roots) fluid passages. Mostly just dead woody stem tissue split. [But get other opinions].