We report on the discovery and spectroscopic confirmation of TOI-2458 b, a transiting mini-Neptune around an F-type star leaving the main-sequence with a mass of M★ = 1.05 ± 0.03 M⊙, a radius of R★ = 1.31 ± 0.03 R⊙, an effective temperature of Teff = 6005 ± 50 K, and a metallicity of ‑0.10 ± 0.05 dex. By combining TESS photometry with high-resolution spectra acquired with the HARPS spectrograph, we found that the transiting planet has an orbital period of ‑3.74 days, a mass of Mp = 13.31 ± 0.99 M⊕ and a radius of Rp = 2.83 ± 0.20 R⊕. The host star TOI-2458 shows a short activity cycle of ~54 days revealed in the HARPS S-index and Ha times series. We took the opportunity to investigate other F stars showing activity cycle periods comparable to that of TOI-2458 and found that they have shorter rotation periods than would be expected based on the gyrochronology predictions. In addition, we determined TOI-2458's stellar inclination angle to be i* = 10.6‑10.6+13.3 degrees. We discuss that both phenomena (fast stellar rotation and planet orbit inclination) could be explained by in situ formation of a hot Jupiter interior to TOI-2458 b. It is plausible that this hot Jupiter was recently engulfed by the star. Analysis of HARPS spectra has identified the presence of another planet with a period of P = 16.55 ± 0.06 days and a minimum mass of Mp sin i = 10.22 ± 1.90 M⊕. Using dynamical stability analysis, we constrained the mass of this planet to the range Mc ≃ (10, 25) M⊕.