www.pestscience.gr

The above connects to a Greek website that has little to no bearing on the OP's concerns.

Heavy cone production with conifers is often associated with mast years as well as often occurring at times of stress (heat, drought).

It is usual for better nurseries and garden centers to provide plant tags with both the common name (Italian cypress) as well as the proper botanical name - Cupressus sempervirens. But box stores and discount outlets often do not and frequently sell mislabeled plants as well. The cones clearly indicate a cypress and the growth habit leans toward an Italian cypress but not clear enough to state for certain.