The emergence of novel mobile ecosystems, such as mulsemedia and metaverse, has encouraged the evolution of cloudification technologies to accommodate the increasing demand for user services with advanced in-network computing facilities. In this context, the development of privacy-sensitive heterogeneous hypercomputing (PSHH), also known as the third generation of cloudification, is considered an adequate response to current expectations. This article first investigates the evolution of mobile cloudification to illustrate the necessity and inevitability of the burgeoning PSHH. For further clarification, foundational properties and enablers of such computing platforms are thoroughly identified from two major perspectives: privacy preservation and computing harmonization. A preliminary performance evaluation has been conducted to validate the feasibility and advantages of the computing platform. Subsequently, open research directions are highlighted to realize the maturation of PSHH aligned with the development of next-generation mobile networks.