Sephiroth didn’t kill Aerith.

Sephiroth impaled her through a region of the body that doesn’t completely destroy vital organs (at most damage to the liver/ and large intestine)

Also no blood is lost in the scene so no major blood vessels are damaged.

Her spine was severed at a point where the brain still functions to control the heart and lungs, however it paralyses her in the legs and abdomen (which is why she slumps over)

Do to immense pain and swelling of blood vessels do to being impaled, she falls unconscious though still alive.

When laid to a watery rest she immediately sinks (but dead bodies float) Implying body muscle tension is disrupting buoyancy.

Cloud drowned Aerith.