I was thinking about sifting the soil of my garden, going from this:
Are there any benefits in doing so? My goal is to grow vegetables in that soil
I got pretty rocky soil myself. The only benefits I see would be for root crops - especially potatoes and carrots.
Overall the rocks improve drainage and don't pose big problems for most vegetables and tools. The only crops you need to look out for are root vegetables. Carrots in particular can get pretty deformed by rocks in their path. Still perfectly edible just not shop pretty and harder to handle in the kitchen (there are varieties that don't grow very long though like "Paris Market" or "Duwicker" which circumvent the problem). Similar with potatoes.
Getting a decent amount of quality compost in there would probably yield bigger benefits for less work. Especially as the soil looks quite on the sandy side from the pictures.