pathfinder 2e – Is Trick Magic Item one feat or four?

Trick Magic Item in 1 Feat

Trick Magic Item is a single skill feat. You can read it on page 268 of the Core Rulebook where it appears printed only once.

The text of the feat makes it clear that this feat applies to all 4 magical tradition skills (Arcana, Occultism, Nature, and Religion). There is plenty of precedent for this, such as the Quick Recognition skill feat1.

It sounds like part of your confusion stems from how you located the feat on the Archives of Nethys. Odds are the site’s developers added Trick Magic Item to lists for each of those four skills, so that users could find it where they intuitively expect it to be. It’s an artifact of representing a book within a database table.

1 For an list with more examples, see Ifusas’s answer.