  We continue our study of bilinear estimates on waveguide $\mathbb{R}\times
\mathbb{T}$ started in \cite{DFYZZ2024,Deng2023}. The main point of the current
article is, comparing to previous work \cite{Deng2023}, that we obtain
estimates beyond the semiclassical time regime. Our estimate is sharp in the
sense that one can construct examples which saturate this estimate.
