Sorting using comparison is superlinear or sublinear?
In complexity theory, the input size is by convention (or definition, really) the number of cells the input takes up on a Turing machine tape.

The famous $\Omega(n \log n)$ bound does not adhere to this convention, though; $n$ is not input size but number of elements here. The input is (in general) longer than that since every element will have to be encoded on the tape in some way.

Generally, in sorting we consider the input to be the array (or list) of elements to be sorted. We don't pass the comparison matrix.

But you touch on an important point: complexity statements depend on machine model and input encoding. We usually default to TMs or RAMs depending on context and "reasonable" (i.e. not wasteful) encodings, but if there is any chance for ambiguity you need to state all the parameters.

For instance, the input size of sorting is $n$ is you consider RAMs with unit cost measure!