Herbs are not a staple food for hamsters, but as an extra. If you offer a herbs mix you will therefore see that your hamster only takes the things from this mix that he needs and will leave the rest.
Herbs must always be dried in a special way, otherwise all nutrients are gone and only dry fibers remain. Hamster can smell and taste this. Therefore, such herbs are not eaten.
Herbs are certainly a nice enrichment of the food and if you know how to put together the right mix, your hamster can choose according to his own needs.