The $beta$ intensity distributions of the decays of $^{100text{gs},100text{m}}$Nb and $^{102text{gs},102text{m}}$Nb have been determined using the Total Absorption $gamma$-Ray Spectroscopy technique. The JYFLTRAP double Penning trap system was employed to disentangle the isomeric states involved, lying very close in energy, in a campaign of challenging measurements performed with the Decay Total Absorption $gamma$-ray Spectrometer at the Ion Guide Isotope Separator On-Line facility in Jyvaskyla. The low-spin isomeric state of each niobium case was populated through the decay of the zirconium parent, that was treated as a contaminant. We have applied a method to extract this contamination, and additionally we have obtained $beta$ intensity distributions for these zirconium decays. The $beta$-strength distributions evaluated with these results were compared with calculations in quasiparticle random-phase approximation, suggesting a prolate configuration for the ground states of $^{100,102}$Zr. The footprint of the Pandemonium effect was found when comparing our results for the analyses of the niobium isotopes with previous decay data. The $beta$-intensities of the decay of $^{102text{m}}$Nb were obtained for the first time. A careful evaluation of the uncertainties was carried out, and the consistency of our results was validated taking advantage of the segmentation of our spectrometer. The final results were used as input in reactor summation calculations. A large impact on antineutrino spectrum calculations was already reported and here we detail the significant impact on decay heat calculations.
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