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With the rapid advancement of DNNs, numerous Process-in-Memory (PIM) architectures based on various memory technologies (Non-Volatile (NVM)/Volatile Memory) have been developed to accelerate AI workloads. Magnetic Random Access Memory (MRAM) is highly promising among NVMs due to its zero standby leakage, fast write/read speeds, CMOS compatibility, and high memory density. However, existing MRAM technologies such as spin-transfer torque MRAM (STT-MRAM) and spin-orbit torque MRAM (SOT-MRAM), have inherent limitations. STT-MRAM faces high write current requirements, while SOT-MRAM introduces significant area overhead due to additional access transistors. The new STT-assisted-SOT (SAS) MRAM provides an area-efficient alternative by sharing one write access transistor for multiple magnetic tunnel junctions (MTJs). This work presents the first fully digital processing-in-SAS-MRAM system to enable 8-bit floating-point (FP8) neural network inference with an application in on-device session-based recommender system. A SAS-MRAM device prototype is fabricated with 4 MTJs sharing the same SOT metal line. The proposed SAS-MRAM-based PIM macro is designed in TSMC 28nm technology. It achieves 15.31 TOPS/W energy efficiency and 269 GOPS performance for FP8 operations at 700 MHz. Compared to state-of-the-art recommender systems for the same popular YooChoose dataset, it demonstrates a 86 ×, 1.8 ×, and 1.12 × higher energy efficiency than that of GPU, SRAM-PIM, and ReRAM-PIM, respectively.