Strong-field ionization provides a fundamental route for probing nonlinear electron dynamics on ultrafast time scales, but it has been explored almost exclusively with classical coherent driving fields. Intense quantum light sources, particularly bright squeezed vacuum (BSV), now make it possible to ask how macroscopic photon-number fluctuations affect nonperturbative electron emission. Here we address this question by performing shot-resolved BSV–photoelectron coincidence measurements in strong-field ionization of xenon atoms, with simultaneous access to the single-shot driving intensity and the energy- and momentum-resolved photoelectron response. By calibrating the intensity-dependent ionization probability with a pulse-integrated ADK response, we reconstruct the single-pulse ionization-yield distribution and quantify its fluctuations in electron momentum space. We find that intensity-conditioned BSV-driven spectra recover coherent-field-like cutoff scaling, while the reconstructed yield fluctuations increase toward higher electron energies and momenta, showing that high-energy electrons preferentially sample rare high-intensity BSV shots. Beyond ensemble-averaged spectra or photoelectron-number statistics, this approach resolves the momentum- and energy-dependent transfer of quantum-light fluctuations into atomic ionization yields. These results establish yield fluctuations as observables for strong-field quantum optics and benchmarks for theories beyond the classical-field approximation.