Lawn damage after treatment - Roll turf approximately 2 years old

There are grass varieties that simply have shallow roots regardless of watering. I would rule out fertilizer damage. Otherwise, it would not turn green again after one or two waterings. Fertilizer damage is dead. I managed it myself last week on two [Stennen].

I have overseeded evenly

With a roll lawn, nothing needs to be overseeded.

Yes. Regular overseeding results in a good lawn. Or you want to strengthen or establish other lawn varieties.

That’s not a dust desert yet, depending on your standards, you can just leave it like that. I always do that too, it turns green again in wetter times. And I even park my G-Class there ;).

Yes. Regular overseeding results in a good lawn. Or you want to strengthen or establish other grass varieties.

Where are the additional seeds supposed to germinate if I already have a nice and, above all, dense turf?

There are always some gaps. Also, mowing low then works without problems.
Turf is not as dense as a golf green…
I only did it to establish other varieties. Or in places where, for example, I spilled fertilizer.