The removed topsoil has produced the first garden plant, as we noticed at the beginning of August. After a little more than 2 weeks, half the pile is overgrown.
Recommendation: Pull out and cover the pile of soil with a dark, waterproof tarp.
Unfortunately, I read this tip too late here in the forum.
In the meantime, I am struggling to tear out that stuff while spreading the topsoil and to remove the roots. They are really quite stubborn.