Is $Ω(n\log ⁡n)$ the lower-bound for *all* sorting algorithms or *just comparison-based* sorting algorithms?

Question

Is $Ω(n\log n)$ the lower-bound for all sorting algorithms or just comparison-based sorting algorithms?

If the latter, is it possible for there to be general-purpose sorting algorithms which perform better than $Ω(n\log n)$?

General-purpose, for example, means you aren't assuming elements have a fixed number of bits.

The input to the algorithm is a sequence of $n$ bits. The bits are an encoding of integers.