That is not a rotary tiller. Harrowing afterwards is too rough for sowing. Harrow, sow, roll. Either do not water at all and hope for rain or water daily if there is no rain. Do not let it dry out. The newly germinated grass does not like that at all.
I have another stupid question about the preparation.
As can be seen in the pictures (below), our humus has already been leveled with a small excavator. Should I still break it up completely with a power tiller and lightly press it down with a roller, or leave it as it is and only roughen the top layer with a rake?
PS: In some places, you currently sink about 1 cm, in other places not at all.
How loosened should the soil be? During leveling, it was completely loosened and then compacted again by the excavator bucket, so it is now relatively firm.
I now fear that if I "only" loosen the top 2-3 cm with the rake, it will be too little.
Lawn, when freshly sown, needs moist soil but no waterlogging. Does the soil allow water to pass through? If yes, raking is sufficient. If no, loosen deeply with a rotary tiller or cultivator.