Spectroscopic time series and GLS periodogram. Left: HARPS-N spectroscopic time series analysed in this work. From top to bottom, the panels show the RVs, RV residuals, BIS, log $R_{HK}^{\text{'}}$, and Hα measurements. In the log $R_{HK}^{\text{'}}$ panel, a sinusoidal modulation – plotted as a black dashed line – is visible, suggesting the presence of a stellar activity cycle, consistent with the period identified in the corresponding GLS periodogram. Right: GLS periodograms of the RVs and the spectroscopic activity indicators. The primary peak in each periodogram is marked with a vertical black dashed line. The vertical blue shaded area highlights the period signal at 3.981 days, consistent with the transit-like periodicity identified in the TLS analysis. The horizontal dash-dotted and dotted lines mark, respectively, the 0.1% and the 1% FAP levels as evaluated using the bootstrap method.