The top layer definitely only sifted soil on it. It's not worth the trouble with roots and stones that also come to the surface afterwards.
Sifting yourself is in my opinion not worth it. Sifted topsoil is simply too cheap. I think we paid 20€ gross per cubic meter including delivery and installation.
Whaaaat? Last Saturday I picked up topsoil with a trailer at the gravel plant... Cost: 33 EUR net per tonne! Oh, probably caught the wrong region.
I would get new soil. Sifting it yourself: that probably removes roots and larger stones, but unfortunately not the weed seeds. With purchased soil, this was eliminated through thermal treatment (make sure to inquire about this!!!), so the bed or lawn is at least weed-free at the beginning.
With purchased soil, this was destroyed by means of thermal treatment (definitely inquire about that!!!), so the bed, the lawn is at least weed-free at the beginning.
... and many good components of the soil as well. From my experience, I would therefore never use screened soil,