What is the purpose/function of this power inductor in parallel?

It's a "power" inductor because it needs to carry a significant amount of DC current. Connecting the windings in parallel gives you the same inductance as either winding alone, but with twice the current capacity and half the DC resistance. It's exactly equivalent to a simple coil with the same number of turns, but twice the cross-sectional area of the wire.

Unless the designer is here, there is no way to really know for certain. Perhaps it was a cheaper option. Maybe it had the best performance under tests conditions compared with other inductors?

If the company that designed this already use that component in another design, it makes sense to re-use it on another product. It saves having to buy a new component, and could reduce the price of the current one if they then have to purchase a higher quantity.

In some products I have designed I have used inductors for many different reasons. Some of them the reason I mentioned above. We already stocked that part and it happened to be the same value as I needed, so I used that.

Sometimes I just follow the datasheets of certain ICs and use recommended parts. This could have been any one of my suggestions above, or possibly something else.

Other time, I have just used a cheap one where things aren't performance critical. Other times I have needed performance so have tested the device with different parts and chose the one that worked best. I don;t think there will be a definitive answer unless the designer happens to come by. But the reasons I suggested are quite common.

Look into the Bourns SRF1260 datasheet: Multiple applications: parallel, series, dual-inductor and transformer.

Clearly the designer opted for parallel connection, thus doubling the current rating.