Разобрался, цикл был не нужен.
Меняем
def write_to_csv(property):
with open('cian_parser.csv', 'a', encoding='utf8', newline='') as file:
#...
на
def write_to_csv(property):
with open('cian_parser.csv', 'w', encoding='utf8', newline='') as file:
#...
