Interstitial oxygen order and its competition with superconductivity in La$_2$PrNi$_2$O$_{7+\delta}$

High-temperature superconductivity in bilayer nickelate La$_3$Ni$_2$O$_7$ under pressure has attracted significant interest in condensed matter physics. While early samples exhibited limited superconducting volume fractions, Pr substitution for La enabled bulk superconductivity in polycrystals under pressure and enhanced transition temperatures in thin films at ambient pressure. Beyond rare-earth doping, moderate oxygen or ozone annealing improves superconductivity by mitigating oxygen vacancies, whereas high-pressure oxygen annealing leads to a trivial, non-superconducting metallic state across all pressure regimes. These findings highlight the need to elucidate both the individual and combined effects of Pr doping and oxygen stoichiometry in modulating superconductivity in bilayer nickelates. Here, using multislice electron ptychography and electron energy-loss spectroscopy, we investigate the structural and electronic properties of as-grown La$_2$PrNi$_2$O$_7$ and high-pressure-oxygen-annealed La$_2$PrNi$_2$O$_{7+\delta}$ polycrystals. We find that Pr dopants preferentially occupy outer La sites, effectively eliminating inner-apical oxygen vacancies and ensuring near-stoichiometry in as-grown La$_2$PrNi$_2$O$_7$ that is bulk-superconducting under pressure. In contrast, high-pressure oxygen annealing induces a striped interstitial oxygen order, introducing quasi-1D lattice potentials and excess hole carriers into p-d hybridized orbitals, ultimately suppressing superconductivity. This behavior starkly contrasts with cuprate superconductors, where similar interstitial oxygen ordering enhances superconductivity instead. Our findings reveal a competition between striped interstitial oxygen order and superconductivity in bilayer nickelates, offering key insights into their distinct pairing mechanisms and providing a roadmap for designing more robust superconducting phases.