Is search a binary heap operation?
Actually it depends on your point of view, or level of detail.

The heap, or better priority queue, as abstract data structure usually supports operations like is-empty, add-element, delete-min. And usually not find-element. This is the data structure seen as a specification, fixing the set of operations and their behaviour. The implementation is unknown, it can be a linked tree or array.

The wikipedia page however is concerned with the implementation. That is even clear from the title binary heap. (You understand the binary heap by looking as if it is a tree, you implement it using an array). In this implementation it is easily seen how to program your operation find-element. Technically, that is another abstract data structure (as it has an additional operation aprt from standard heap operations).

In practice heaps (priority queues) are often used for graph algorithms like Dijkstra. There it is important that the priorities stored in the heap can be changed (if we find a shorter route). That is only possible if we are able to find the element in the heap so we can adjust its priority (and reposition the element in the heap). Usually that is done by building another structure on top of the heap so we can efficiently find the positions where elements are stored.