2pf in single-trace $T\bar{T}$ holography

The 2pf in single-trace $T\bar{T}$ holography was computed and analyzed for operators in the $w=0$ sector in~\cite{Asrat:2017tzd}. Here we present its immediate generalization to non-zero winding $w$. For long strings, the result is identical to the one obtained within the TsT/$T\bar{T}$ approach in~\cite{Cui:2023jrb} (up to a factor of the reflection coefficient).