We present an extensive optical/NIR spectroscopic campaign of the black hole transient Swift J1727.8-1613 during its 2023–2024 discovery outburst, using 13 mid/high resolution spectra obtained with VLT/X-Shooter. The observations trace the system through its hard-to-soft and soft-to-hard state transitions. We report the detection of sporadic, symmetric absorption troughs in Balmer emission line wings during the bright states, which we interpret as signatures of optically thick regions within the accretion disc rather than a wind. Through analysis of the He\,\textsc{ii} $\lambda4686$ \AA\ line, which is a good tracer of the chromospheric emission from the disc, we identify a distinct morphological change during the peak of the radio flaring period, consistent with the re-ionization of the outer disc probably associated with a discrete jet ejection. Finally, we detect the emergence of the spectroscopic signatures from a massive, cool accretion disc wind during the transition back to the low-hard state. This outflow manifests as broad blue-shifted absorption lines, unequivocally detected in higher-order lines from the Balmer series, with a characteristic velocity of $\approx$750\,km\,s$^{-1}$, which is thought to be absorbing the blue component from a disc-formed line in He\,\textsc{ii} $\lambda4686$ \AA during this epoch.