The $\beta$ decays of the ground state (gs) and isomeric state (m) of $^{96}$Y have been studied with the total absorption $\gamma$-ray spectroscopy technique at the Ion Guide Isotope Separator On-Line facility. The separation of the 8$^{+}$ isomeric state from the 0$^{-}$ ground state was achieved thanks to the purification capabilities of the JYFLTRAP double Penning trap system. The $\beta$-intensity distributions of both decays have been independently determined. In the analyses the de-excitation of the 1581.6 keV level in $^{96}$Zr, in which conversion electron emission competes with pair production, has been carefully considered and found to have significant impact on the $\beta$-detector efficiency, influencing the $\beta$-intensity distribution obtained. Our results for $^{96\text{gs}}$Y (0$^+$) confirm the large ground state to ground state $\beta$-intensity probability, although a slightly larger value than reported in previous studies was obtained, amounting to $96.6_{-2.1}^{+0.3}\%$ of the total $\beta$ intensity. Given that the decay of $^{96\text{gs}}$Y is the second most important contributor to the reactor antineutrino spectrum between 5 and 7 MeV, the impact of the present results on reactor antineutrino summation calculations has been evaluated. In the decay of $^{96\text{m}}$Y (8$^{+}$), previously undetected $\beta$ intensity in transitions to states above 6 MeV has been observed. This shows the importance of total absorption $\gamma$-ray spectroscopy measurements of $\beta$ decays with highly fragmented de-excitation patterns. $^{96\text{m}}$Y (8$^{+}$) is a major contributor to reactor decay heat in uranium-plutonium and thorium-uranium fuels around 10 s after fission pulses, and the newly measured average $\beta$ and $\gamma$ energies differ significantly from the previous values in evaluated databases (...)
