On the deep seafloor, why do gas bubbles in lava stay small while surface lava bursts into ash?

Answer: Surrounding pressure squeezes them

Surrounding pressure squeezes them ✓ — Right — surrounding pressure is the key. Seawater adds about one atmosphere every 10 m, so each meter of descent presses bubbles tighter. They want to expand; the water column won't let them. On deep ridges that 'lid' is strong enough that most eruptions only ooze — like squeezing toothpaste, not popping a soda can.

Cold water hardens bubble walls — Cold water hardening the bubble walls sounds plausible, but gases stay trapped because of external pressure, not stiffer walls. Temperature mainly affects how the lava flows; it's why pillow lavas form a glassy skin on the deep ridge, not why the gas can't escape.

Deep lava holds less dissolved gas — Less dissolved gas at depth has cause and effect backward. The same magma actually exsolves more gas as it rises and the pressure drops. The difference between deep and shallow eruptions is whether bubbles can expand, not whether the gas is there.