I cannot for the life of me decide if this is supposed to be interpreted as a complement clause or an embedded question or what.

My thought process so far is that it couldn't be a reported question (for semantic reasons) or fused relative ("how" here doesn't work as a relative pronoun) at all. Sources I've checked so far have been ambiguous about how small or vast a category "complement clause" can encompass, for example, with some including reported questions in the category of verbal complements (Mark Newson et al., 2006) and some not doing so.

Edit: I'll add the context in which the sentence originally appeared, after talking with my student. I believe this doesn't fundamentally change anything, but perhaps pushes it towards an interrogative interpretation:

You may complain about our high prices, but unlike a certain competitor, we have informed you that the increase would be 15%, so at least we know how expensive we are.

I cannot for the life of me decide if this is supposed to be interpreted as a complement clause or an embedded question or what.

My thought process so far is that it couldn't be a reported question (for semantic reasons) or fused relative ("how" here doesn't work as a relative pronoun) at all. Sources I've checked so far have been ambiguous about how small or vast a category "complement clause" can encompass, for example, with some including reported questions in the category of verbal complements (Mark Newson et al., 2006) and some not doing so.

Edit: I'll add the context in which the sentence originally appeared, after talking with my student. I believe this doesn't fundamentally change anything, but perhaps pushes it towards an interrogative interpretation:

You may complain about our high prices, but unlike a certain competitor, we have informed you that the increase would be 15%, so at least we know how expensive we are.

I cannot for the life of me decide if this is supposed to be interpreted as a complement clause or an embedded question or what.

My thought process so far is that it couldn't be a reported question (for semantic reasons) or fused relative ("how" here doesn't work as a relative pronoun) at all. Sources I've checked so far have been ambiguous about how small or vast a category "complement clause" can encompass, for example, with some including reported questions in the category of verbal complements (Mark Newson et al., 2006) and some not doing so.

Edit: I'll add the context in which the sentence originally appeared, after talking with my student. I believe this doesn't fundamentally change anything, but perhaps pushes it towards an interrogative interpretation:

You may complain about our high prices, but unlike a certain competitor, we have informed you that the increase would be 15%, so at least we know how expensive we are.

I cannot for the life of me decide if this is supposed to be interpreted as a complement clause or an embedded question or what.

My thought process so far is that it couldn't be a reported question (for semantic reasons) or fused relative ("how" here doesn't work as a relative pronoun) at all. Sources I've checked so far have been ambiguous about how small or vast a category "complement clause" can encompass, for example, with some including reported questions in the category of verbal complements (Mark Newson et al., 2006) and some not doing so.

Edit: I'll add the context in which the sentence originally appeared, after talking with my student. I believe this doesn't fundamentally change anything, but perhaps pushes it towards an interrogative interpretation:

You may complain about our high prices, but unlike a certain competitor, we have informed you that the increase would be 15%, so at least we know how expensive we are.