No, eggs are not berries.
What is a Berry?
Before we definitively answer the question, let's define what a berry is. Botanically, a berry is a fruit produced from a single flower with one ovary, containing seeds. Think strawberries, blueberries, and tomatoes (yes, tomatoes are berries!). These fruits develop from the flower's ovary and contain seeds within a fleshy pulp.
Why Eggs Aren't Berries
Eggs, on the other hand, are animal products. They are produced by birds (and other animals) as a means of reproduction. They contain the genetic material necessary to create a new organism, not seeds for a plant. The reference material clearly states that an egg is a protein and an animal product, explicitly stating it is neither a fruit nor a vegetable.
Therefore, based on the botanical definition of a berry and the biological nature of an egg, there's no overlap. They are fundamentally different things.