Van Hove Singularities, Superconductivity, and the Josephson Diode Effect in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>NiTe</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> <

Superconductivity in the transition-metal dichalcogenide PdTe_{2} has been attributed to the proximity of a three-dimensional Van Hove singularity to the Fermi level. In isostructural NiTe_{2}, recently used as the weak link in a Josephson diode, a similar Van Hove singularity has been predicted to occur, but superconductivity is mysteriously absent. Using bulk-sensitive soft x-ray angle-resolved photoemission spectroscopy, we reveal that this Van Hove singularity lies even closer to the Fermi level in NiTe_{2} than in PdTe_{2}. To explain the lack of superconductivity in NiTe_{2}, we perform ab initio calculations incorporating the Kukkonen Overhauser interaction, showing that an incipient magnetic instability suppresses superconductivity at an unprecedented scale. Finally, we present a tight-binding model that links the Van Hove singularity to a sign change in the Josephson diode effect at small magnetic fields, suggesting a new mechanism for Josephson diodes.