As long as you are not on a suppressive progestin this should not interfere with the AMH.
Birth control shuts down ovulation, keeping the remaining ovarian follicles quiet and small so AMH is artificially lowered, but body identical estradiol and micronised progesterone in typically prescribed doses do not cause this.
However the clinical utility of AMH in someone with ovarian aging advanced enough to require menopause hormone therapy is questionable unless there were special circumstances such as POI or young women with chemotherapy etc.