High levels of proteins in a cell culture primarily indicate that the cells have an increased capacity for protein synthesis, which is typically associated with the presence of ribosomes. Ribosomes are the cellular machinery responsible for translating messenger RNA (mRNA) into proteins.
Therefore, the most relevant conclusion you can draw from the presence of very high levels of proteins is:
They have ribosomes.
While other factors like higher cytoplasm volume or increased ATP production (related to metabolic activity) might also be present in cells that synthesize a lot of proteins, the direct correlation with protein levels is most accurately associated with ribosomes.