Anyway, basically what I am saying is that "omniscience" is a self-contradictory concept
Not true.
Omniscience is a consequence of a being which is absolutely literally infinite.
If there is nothing he doesn't know
yes...
then he must know that he doesn't know what is like not to know
no. An all-knowing God knows what it is like not to know, just as it knows 3-wheeled-bicycles, and non-dairy milk. It's just a contradictory concept like any other.
Another way of considering it, is from the perspective of a creator-god which is similar to the author of a book. The author can write a book where the protagonist is deaf-mute, but the author themself is neither deaf nor mute. A creator-god can create the conceppt "absence of knowledge" and then it knows "the absence of knowledge" while still remaining to be all-knowing itself. "Absence of knowledge" is just a concept like any character in any book by any author. The book in this analogy is "reality".
Here's a specific example: the flux-capacitor from Back-to-the-future. It's a concept which the screenwriter created. A creator god can create any concept. One of those concepts could be "what it's like not to know". Once the creator-god creates it, it knows it. It knows "what it's like not to know" because it created it. It's as simple as that.
Contradiction resolved.