It only makes sense for a little Kitsune like Tails to own a lab coat, it protects his fur from his experiments and working with mechanical parts, oil isn't easy to get out of fur

Tails' lab coat is a five stub button enclosure medium length with one breast pocket and two thigh pockets and long sleeves, his coat also includes a rear vent

Tails often likes to wear his lab coat as it makes him happy, and it's quite cosy

Tails has been known to wear his lab coat while out of his workshop and home in Mystic Ruins

he also had a lab coat before which was a size too big for him which made wearing it around machinary sometimes a hazard
he keeps his old coat out of pure nostalgia