the extent to which I was full of it

[Maybo]

Katherine raised an eyebrow, undecided on the extent to which I was full of it. “Mold?” “Black mold,” I said. “We had a person come look at it. An inspector.”

Source: The September House by Carissa Orlando

Why is “which” used and not “what?

 

[Skrej]

Because it's not a question of what she's full of, it's a question of how full of it she is.

It's also a set expression the extent to which...

 

[tedmc]

An extent is a measure of a limit. I think "which" describes a quantitative measure better than "what".

 

[jutfrank]

You can't use 'what' in relative clauses like this. Only 'which' is correct.