Dismantling of slurry cellar / Preparation for lawn planting

first remove 30 cm and then refill with topsoil?

You won't gain anything from that, as the "new" topsoil is usually also full of weed seeds and root pieces.

What would you recommend to get the roughest draw as much as possible?

I didn't do anything at all. Neither removed nor fought. Topsoil was free of visible weeds, leveled and seeded and planted on top. Weeds are present, I would say they all flew in - except for the oats, they have eternal life.

For the next construction phase, the chamomile will fall victim to the scythe, I will dig out the larger plants and that's it.

Couch grass rhizomes, if present, rake to the surface and let dry out. Otherwise, simply lay the lawn; if properly maintained, it will suppress most of it.