The reason why the "Mug" and the "Amazon Card" do not appear in the product list from Inventory, Sales or Purchase, is because the rewards belong to a different model in this case "hr.referral.reward" and the products that you see in the other apps could belong to "product.template" or "product.product". 

But you might wonder why the rewards are categorized under different models.

It's because we aim to prevent any distractions for our logistics team. Instead of having them handle rewards like mugs or Amazon gift cards for our employees, we want them to focus solely on delivering the correct products, in the right quantities, to the right places, and on time for our company's clients.

If rewards shared the same model, Odoo would generate a delivery order to our logistics team each time someone requested their reward.

However, to streamline the responsibility for delivering rewards, you can assign a gift manager in the reward form view.

Odoo will schedule an activity to remind the responsible to deliver the reward each time a user requests it.

Disclaimer: This is not an official documentation.