smin = -1;
h[z_] := Exp[-z/2]
smax=zmax/.Last @ Reap[
    NDSolveValue[
        {
        int'[z] == (Exp[z] - 1) h[z], int[smin] == 0,
        WhenEvent[int[z]==0, {"StopIntegration", Sow[z, "zmax"]}]
        },
        int,
        {z, smin, Infinity}
    ],
    _,
    #1 -> First@#2&
]

sol = Last@
  Reap[NDSolveValue[{int'[z] == (Exp[z] - 1) h[z], int[smin] == 0,
     WhenEvent[int[z] == 0, {"StopIntegration", Sow[z, "zmax"]}]},
int, {z, smin, Infinity}], _, #1 -> First@#2 &]
smax = zmax /. First@sol

sol = Last@
  Reap[NDSolveValue[{int'[z] == (Exp[z] - 1) h[z], int[smin] == 0,
     WhenEvent[int[z] == 0, {"StopIntegration", Sow[z, "zmax"]}]},
int, {z, smin, Infinity}], _, #1 -> First@#2 &]
smax = zmax /.sol

smax = Hold[
  zmax /. Last@
Reap[NDSolveValue[{int'[z] == (Exp[z] - 1) h[z], int[smin] == 0,
   WhenEvent[int[z] == 0, {"StopIntegration", Sow[z, "zmax"]}]},
  int, {z, smin, Infinity}], _, #1 -> First@#2 &]
]