Lawn reinstallation in autumn or spring with deciduous trees

In principle, it is actually enough to mow briefly and smooth (whether sand or topsoil I would depend on how heavy the soil is). This is then called Sandwich Technique and works well. I have done this in several places and it worked very well. The result gets even better if you scarify at the lowest level…

to the original question: so rather wait until spring?

Well, that's betting on the weather... if you believe in a relaxed, wet, and warm winter: autumn. However, I would personally wait for spring...

If you do not choose [Rollrasen], I would not do it in the fall. In the spring, then reseed again. Then mow, fertilize, water, and do it quite regularly. Often change the blades on the robot.

If you don't decide on turf, I wouldn't do it in autumn. Then reseed again in spring. ...

Two no's result in the following statement: If sowing, then spring? ;) So if sowing: sow in spring and reseed in early summer?

should be "still in autumn". Then sow over again in spring.