meaning of "ironic detachment"
A critic talking about A. S. Byatt's book "The Biographer’s Tale" says that

"We give ourselves up to the illusion the book sets up, taking us into the mind of its subject and thence into that of his subject and again into the minds of his subjects – once ‘real’ people, Linnaeus, Galton and Ibsen, all of whom
were famous for creating their own taxonomies and fictions.But even as we do so, we know that the book we hold in our hands is a fiction created by Byatt and we are aware of her ironic detachment hovering over the whole."

What does it mean "her ironic detachment"?

Question

meaning of "ironic detachment"
A critic talking about A. S. Byatt's book "The Biographer’s Tale" says that

"We give ourselves up to the illusion the book sets up, taking us into the mind of its subject and thence into that of his subject and again into the minds of his subjects – once ‘real’ people, Linnaeus, Galton and Ibsen, all of whom
were famous for creating their own taxonomies and fictions.But even as we do so, we know that the book we hold in our hands is a fiction created by Byatt and we are aware of her ironic detachment hovering over the whole."

What does it mean "her ironic detachment"?

Answer

"Detachment" means that someone is not emotionally involved in the thing they are describing.

If I am describing ants on a sidewalk, I am detached about it because I'm not an ant and I don't care about ants. If I am describing people on a sidewalk, I probably am involved because I'm human and I care about humans. However, we can be detached when we are speaking about humans.

"Ironic" can mean a form of bitter humor in which you say the exact opposite of what you really mean. For example, you look at a hamburger and say "Well, this certainly is gourmet food."

In the case of sophisticated writer, it probably means that Byatt feels something a little different from what she is saying--and that we are able to understand what she really means.

Answer

My interpretation is that author Byatt has a detached prose style, so that the reader finds it ironic because he is compellingly engaged as he gets into the story("illusions") and expects the same kind of engaging writing style but realizes it is the opposite.

So the detachment is ironic, that is, the story is quite engaging but the writing style is detached.