Why can eruptions that form a large igneous province, a huge region of volcanic rock, harm marine life far from the lava?

Answer: Released gases change climate and seawater chemistry worldwide

Released gases change climate and seawater chemistry worldwide ✓ — Gases released during massive volcanic episodes can change the atmosphere and oceans far beyond the lava fields. Carbon dioxide traps heat, and some dissolves in seawater, increasing its acidity. Warming can also reduce oxygen availability, so distant marine life can face several stresses without ever touching lava.

Deposited ash blocks nearby bays and traps marine life — Ash blocking nearby bays cannot explain damage across distant oceans. Ash may affect local water and supply nutrients, but a local obstruction is not a worldwide transmission route. Volcanic gases can spread through the atmosphere and change ocean conditions far from the eruption.

Ocean currents carry the lava's heat to distant seas — Direct heat from lava carried by currents is not the main route to worldwide marine damage. That heat disperses near the eruption, whereas added greenhouse gases alter the planet's energy balance. The ocean warms broadly through climate change, with accompanying changes in acidity and oxygen.