У карты даже есть название MEU 2

Это обычный внж супруга европейца и никаких прав на поездки в Шенген без визы не дает. Вы бьетесь в закрытую дверь, надеясь найти проход, которого нет 3. Residence card for family members of a Union citizen that are not citizens of a Union Member State/ MEU2 Family members of an EU citizen who are not EU citizens must apply for a residence card within 4 months of their arrival date in the Republic. Information on the documents required, depending on the reason for staying, can be found by following the appropriate link. https://www.gov.cy/moi/en/residence-cards/#:~:text=The%20card%20issued%20to%20family,of%20receipt%20of%20the%20application.