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 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.

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.