What is the "idiomatic" way of recreating this topology?

If you play around with simple Shapes (Elipses, Circles) and then loft between the rotated sketches you can produce fairly similar effects.
You model half of a point with three sketches.
Loft between two using the third as the loft path.
Then mirror the body to make a full point.
Rotate tool with ‘copy’ by 72 degrees to produce 5 points.
Boolean all five.
Fillet edges to smooth.
This is not exact because you do not get the flat face like a balloon, but it will give you ‘food for thought’.
The sketch picture shows the three sketches, one elipse, one circle, and one spline.
Instead of the circle, you could hand draw a spline that will give a much flatter effect on the top and bottom surface of the star.