Radio and high-energy variable emission from a multi-wavelength follow-up of the infant planet-hosting star V1298 Tau

V1298 Tau is a very young and magnetically active K1V star which hosts a benchmark multi-planetary system to study planet formation and evolutionary history at the earliest stages. Between 2025 and 2026, we conducted a campaign to monitor the variability of V1298 Tau in radio (band C), X-ray, and NUV bands, with the support of publicly available contemporary optical light curve, and to investigate multi-band correlations to link the emission with stellar activity. Radio observations were carried out with the Karl G. Jansky Very Large Array (JVLA) in band C (4.5--6.5 GHz). X-ray and NUV observations were carried out with the Swift satellite over 20 days, ending one month before the begin of the radio campaign. We analysed the temporal variability of peak (integrated) fluxes in the C-band and of X-ray (NUV) luminosities on various timescales, comparing it with the variability observed in the high-cadence optical light curve collected by the ASAS-SN survey. We observed both radio and high-energy time variable emission. JVLA detected emission in 90% of the visits, switching between high (at least 0.1 mJy/beam) and low flux states in matter of days or hours. The fluxes show moderate correlation with the optical light curve, suggesting modulation with the stellar rotation period. Except for one visit, dynamic spectral analysis does not reveal short-term (minutes) variability, nor is there any evidence of circularly polarised emissions. Overall, the radio observations can be explained as gyrosynchrotron and/or cyclotron emission from the corona, and linked to stellar magnetic activity. At high-energy, we detected significant variability in X-ray luminosity (within the range 1.2--2.5x10+30 erg/s), the decay phase of a stellar flare, and evidence of correlation with the optical flux. Our data confirm that V1298,Tau follows the near-linear Güdel-Benz relation.