In this work, we present the results from a study of X-ray normal galaxies, that is, galaxies not harbouring active galactic nuclei (AGN), using data from the first complete all-sky scan of the X-ray survey (eRASS1) obtained with eROSITA on board the Spectrum-Roentgen-Gamma observatory. eRASS1 provides the first unbiased X-ray census of local normal galaxies, thus allowing us to study the X-ray emission (0.2-8.0 ) from X-ray binaries (XRBs) and the hot interstellar medium in the full range of stellar population parameters present in the local Universe. By combining the updated version of the Heraklion Extragalactic Catalogue (HECATE v2.0) value-added catalogue of nearby galaxies (Distance ; lesssim \,200$Mpc) with the X-ray data obtained from eRASS1, we studied the integrated X-ray emission from normal galaxies as a function of their star-formation rate ( ), stellar mass ( ), metallicity, and stellar population age. After applying stringent optical and mid-infrared activity classification criteria, we constructed a sample of 18790 bona fide star-forming galaxies (HEC-eR1 galaxy sample) with measurements of their integrated X-ray luminosity (using each galaxy's D$_ $) over the full range of stellar population parameters present in the local Universe. By stacking the X-ray data in bins, we studied the correlation between the average X-ray luminosity and the average stellar population parameters. We also present updated and -metallicity scaling relations based on a completely blind galaxy sample and accounting for the scatter dependence on the The average X-ray spectrum of star-forming galaxies is well described by a power law ($ $) and a thermal plasma component ($kT = 0.70^ $). We find that the integrated X-ray luminosity of the individual HEC-eR1 star-forming galaxies is significantly elevated (reaching $10^ $) with respect to what is expected from the current standard scaling relations. The observed scatter is also significantly larger. This excess persists even when we measured the average luminosity of galaxies in and metallicity bins, and it is stronger (up to $ sim 2$ dex) towards lower s. Our analysis shows that the excess is not the result of the contribution by hot gas, low-mass XRBs, background AGN, low-luminosity AGN (including tidal disruption events), or stochastic sampling of the XRB X-ray luminosity function. We find that while the excess is generally correlated with lower metallicity galaxies, its primary driver is the age of the stellar populations. Our analysis reveals a sub-population of very X-ray luminous starburst galaxies with higher specific SFRs (sSFRs), lower metallicities, and younger stellar populations. This population drives upwards the X-ray scaling relations for star-forming galaxies and has important implications for understanding the population of XRBs contributing in the most X-ray luminous galaxies in the local and high-redshift Universe. These results demonstrate the power of large blind surveys such eRASS1, which can provide a more complete picture of the X-ray emitting galaxy population and their diversity, revealing rare populations of objects and recovering unbiased underlying correlations.