Why can a seabird's salt gland beat its kidney at handling seawater?

Answer: It makes a water-saving brine

It stores extra oxygen for long dives — Extra oxygen storage solves a diving problem, not a salt problem. The clue is the output: brine. Salt glands make concentrated salty fluid, so ions leave with relatively little water instead of forcing the animal to flush salt out as dilute urine.

It speeds up the digestion of food — Faster food digestion is the wrong system. The gland receives salt from blood, not half-digested food. A useful comparison is other salt-gland animals: the same osmotic challenge can be routed through a compact head gland instead of digestion.

It makes a water-saving brine ✓ — Water-saving brine is the point. Bird and reptile salt glands can make hypertonic fluid, letting salt leave in a small water volume. That is why the organ matters beside the kidney: it turns seawater from a dehydration threat into a manageable salt-export problem.