You can definitely find this dynamic in anime, although a lot of the romance stories are about couples getting together rather than an established relationship. “Horimya” and “My Dress Up Darling” are both series which are recent and very popular. They might be close to what you want. Some less popular titles that are more precisely what you described are “An Archedemon’s Dilemma: How to Love Your Elf Bride” and “Shikimori’s Not Just A Cutie”.
You can definitely find this dynamic in anime, although a lot of the romance stories are about couples getting together rather than an established relationship. “Horimya” and “My Dress Up Darling” are both series which are recent and very popular. They might be close to what you want. Some less popular titles that are more precisely what you described are “An Archedemon’s Dilemma: How to Love Your Elf Bride” and “Shikimori’s Not Just A Cutie”.