Top. GLS periodogram of the RV residuals obtained after subtracting the Keplerian signals of the four transiting planets to the HARPS-N detrended RV time series (Sect. 5.3). The most prominent peak is the second harmonic of P_rot,*. The vertical dotted red line marks the signal of TOI-5624 f at ∼ 45 d. Bottom. Same but after further subtracting the signal at ∼ 6.4 d. The signal at ~45 d becomes the most prominent one with the second highest peak being P_rot,*/2.