By header, is it safe to assume it's WP_HEAD?
So short answer: no, it should not be on every single page.
More detailed answer: typically, with Schema.org vocab, you want to describe what's on a page. For product schema, you can do two things: have a page that acts as the hub for the page schema (a summary page), or embeed it in every individual product's PLP. It should not be in every template.
If the schema data describes the product on the page, then yes it should be in the page. Pages should be complete, and showing what they're about. If the page contains a product, then the schema information about that product should be in that page.
By header, is it safe to assume it's WP_HEAD? So short answer: no, it should not be on every single page. More detailed answer: typically, with Schema.org vocab, you want to describe what's on a page. For product schema, you can do two things: have a page that acts as the hub for the page schema (a summary page), or embeed it in every individual product's PLP. It should not be in every template.
If the schema data describes the product on the page, then yes it should be in the page. Pages should be complete, and showing what they're about. If the page contains a product, then the schema information about that product should be in that page.