How can I use Callout to label the segments of a piecewise function?

Clear["Global`*"]

h[x_] := Piecewise[{{Exp[x], 
     x < -1}, {1 - x^2, -1 < x < 1}, {Sin[Pi x], x > 1}}];

plotRng = {-3, 3};

EDIT: Extracting intervals

intervals = {Cases[h[x][[1, All, -1]], _?NumericQ, 2], plotRng} // 
    Flatten // Union // Partition[#, 2, 1] &;

Show[
 Plot[
    Callout[h[x], 
     Simplify[h[x], Less @@ Insert[#, x, 2]] //
       TraditionalForm // ToString,
     Above,
     Appearance -> None,
     Background -> None],
    {x, Sequence @@ #},
    PlotStyle -> Red] & /@
  intervals,
 PlotRange -> {plotRng, Automatic}]

It is possible to nest several Callout:

   ClearAll[x, h];
    h[x_] := Piecewise[{{Exp[x], 
         x < -1}, {1 - x^2, -1 < x < 1}, {Sin[Pi x], x > 1}}];
    Plot[
     Callout[Callout[Callout[h[x], "Exp[x]", -2], "Sin[Pi x]", 2], 
      "1-x^2", {0.3, Above}], {x, -3, 3}]  

Seen in this video of Wolfram Technology Conference 2018.
There is a notebook attached to this video - see Section "parametric Curve Labeling"