Herbal medicinal products are approved medicines with plant-based active ingredients, from St John's wort products to standardized extracts. For reimbursement in private health insurance, a chain of three links counts. You need a practitioner who prescribes, a product with the status of a medicine and a plan clause that covers it. Pure dietary supplements and teas drop out of this chain. They are not medicines, and you pay for them yourself in every plan.
The most common stumbling block is the prescription requirement. Because almost all herbal medicines are available without a prescription, plans that only reimburse prescription-only medicines have no effect here. Plans with strong benefits reimburse medicines prescribed by a doctor regardless of whether they legally require a prescription, and exactly this wording makes the difference in phytotherapy.