With a small sample of fast X-ray transients (FXTs) with multiwavelength counterparts discovered to date, their progenitors and connections to γ-ray bursts (GRBs) and supernovae (SNe) remain ambiguous. Here, we present photometric and spectroscopic observations of SN 2025kg, the SN counterpart to the FXT EP 250108a. At z = 0.17641, this is the closest known SN discovered following an Einstein Probe (EP) FXT. We show that SN 2025kg's optical spectra reveal the hallmark features of a broad-lined Type Ic SN. Its light-curve evolution and expansion velocities are comparable to those of GRB-SNe, including SN 1998bw, and two past FXT-SNe. We present JWST/NIRSpec spectroscopy taken around SN 2025kg's maximum light, and find weak absorption due to He I 1.0830 μm and 2.0581 μm and a broad, unidentified emission feature at ∼4–4.5 μm. Further, we observe broadened Hα in optical data at 42.5 days that is not detected at other epochs, indicating interaction with H-rich material. From its light curve, we derive a 56Ni mass of 0.2–0.6 M⊙. Together with our companion Letter, our broadband data are consistent with a trapped or low-energy (≲1051 erg) jet-driven explosion from a collapsar with a zero-age main-sequence mass of 15–30 M⊙. Finally, we show that the sample of EP FXT-SNe supports past estimates that low-luminosity jets seen through FXTs are more common than successful (GRB) jets, and that similar FXT-like signatures are likely present in at least a few percent of the brightest Type Ic-BL SNe.