Given the proliferation of the massive machine type communication devices (MTCDs) in beyond 5G (B5G) wireless networks, energy harvesting (EH) aided next generation multiple access (NGMA) systems have drawn substantial attention in the context of energy-efficient data sensing and transmission. However, without adaptive time slot (TS) and power allocation schemes, NGMA systems relying on stochastic sampling instants might lead to tardy actions associated both with high age of information (AoI) as well as high power consumption. For mitigating the energy consumption, we exploit a pair of sleep-scheduling policies, namely the multiple vacation (MV) policy and start-up threshold (ST) policy, which are characterized in the context of three typical multiple access protocols, including time-division multiple access (TDMA), frequency-division multiple access (FDMA) and non-orthogonal multiple access (NOMA). Furthermore, we derive closed-form expressions for the MTCD system's peak AoI, which are formulated as the optimization objective under the constraints of EH power, status update rate and stability conditions. An exact linear search based algorithm is proposed for finding the optimal solution by fixing the status update rate. As a design alternative, a low complexity concave-convex procedure (CCP) is also formulated for finding a near-optimal solution relying on the original problem's transformation into a form represented by the difference of two convex problems. Our simulation results show that the proposed algorithms are beneficial in terms of yielding a lower peak AoI at a low power consumption in the context of the multiple access protocols considered.