Fast radio bursts (FRBs) are energetic, millisecond-duration radio pulses observed at extragalactic distances and whose origins are still a subject of heated debate. A fraction of the FRB population have shown repeating bursts, however it's still unclear whether these represent a distinct class of sources. We investigated the bursting behaviour of FRB 20220912A, one of the most active repeating FRBs known thus far. In particular, we focused on its burst energy distribution, linked to the source energetics, and its emission spectrum, with the latter directly related to the underlying emission mechanism. We monitored FRB 20220912A at $408$ MHz with the Northern Cross radio telescope and at $1.4$ GHz using the $32$-m Medicina Grueff radio telescope. Additionally, we conducted $1.2$ GHz observations taken with the upgraded Giant Meter Wave Radio Telescope (uGMRT) searching for a persistent radio source coincident with FRB 20220912A, which included high energy observations in the $0.3$--$10$ keV, $0.4$--$100$ MeV and $0.03$--$30$ GeV energy range. We report 16 new bursts from FRB 20220912A at $408$ MHz during the period between October 16$^ th $ 2022 and December 31$^ st $ 2023. Their cumulative spectral energy distribution follows a power law with slope $ 0.2$ and we measured a repetition rate of $0.19 $ for bursts having a fluence of $ F 17$ Jy ms. Furthermore, we report no detections at $1.4$ GHz for $ F 20$ Jy ms. These non-detections imply an upper limit of $ < -2.3$, with beta being the 408 MHz -- 1.4 GHz spectral index of FRB 20220912A. This is inconsistent with positive beta values found for the only two known cases in which an FRB has been detected in separate spectral bands. We find that FRB 20220912A shows a decline of four orders of magnitude in its bursting activity at $1.4$ GHz over a timescale of one year, while remaining active at $408$ MHz. The cumulative spectral energy distribution (SED) shows a flattening for spectral energy $E_ $ erg Hz$^ $, a feature seen thus far in only two hyperactive repeaters. In particular, we highlight a strong similarity between FRB 20220912A and FRB 20201124A, with respect to both the energy and repetition rate ranges. We also find a radio continuum source with $240 36$ mu Jy flux density at 1.2 GHz, centered on the FRB 20220912A coordinates. Finally, we place an upper limit on the gamma to radio burst efficiency eta to be $ 10^9$ at 99.7<!PCT!> confidence level, in the $0.4$ -- $30$ MeV energy range. The strong similarity between the cumulative energy distributions of FRB 20220912A and FRB 20201124A indicate that bursts from these sources are generated via similar emission mechanisms. Our upper limit on beta suggests that the spectrum of FRB 20220912A is intrinsically narrow-band. The radio continuum source detected at 1.2 GHz is likely due to a star formation environment surrounding the FRB, given the absence of a source compact on millisecond scales brighter than 48 mu Jy beam$^ $ (cit). Finally, the upper limit on the ratio between the gamma and radio burst fluence disfavours a giant flare origin for the radio bursts unlike observed for the Galactic magnetar SGR 1806-20.