Yeah, aperture shape is definitely important, but its complicated because these are not simple optical designs. For odd starbursts you usually want a lens with straight blades and possibly older lens coatings with missing lens hood. Some lenses get odd special flares appearing because of internal reflections (shiny inner body, shiny aperture blades) or light leaks (often the fault of adapters)
The Volna you showed has an aperture shape similar to Pentax M 50mm f1.7. It is a little star-shaped, but only when stopped down
a little. Here is an example:
Cosmic fly by Stolpulus II - Photo 10557733 / 500px
This doesn't necessarily mean crazy starbursts, though.
One thing you could try to get consistent starbursts is a crosshatch filter. Some filters will make starbursts more interesting, but these filters can also become annoying real quick. Here are some of my examples of using an old manual lens with a crosshatch filter:
https://500px.com/photo/61862005 https://500px.com/photo/60424950
With the filter you have advantage that you can rotate it, and there are filters with different effects