Whether they are fertilized depends on the facility that produces eggs and the population of chickens at the time. Cage system housing might produce almost no fertilized eggs because the animals are isolated. That system is however outlawed in some regions of the world because of animal cruelty and the requirements of high amounts of antibiotics to counter the spread of diseases. All other systems produce at least some amount of fertilized eggs, for example because of misgendered roosters becoming part of the general population until they get spotted.

Some people have successfully hatched some supermarket eggs and that is entirely plausible. They are not being hatched by the hens until the nest is full, so they may be laying around for many days before the hen starts sitting on them - they don't need to be kept warm immediately.

So its probably a menstrual product. Very appropriate for a "holy" day, considering menstrual blood is still considered "unclean" in most fundamentalism circles