For seamless and ubiquitous connectivity in 6G, three-dimensional (3D) network design using flourishing unmanned aerial vehicles (UAVs) will be an inevitable task. Notably, integrating terahertz (THz) networks with UAVs remains an open question, despite its immense potential to achieve exceptional flexibility and high capacity. Spurred by this, we delve into the promising 3D network: the multi-UAV radio access network (RAN) with THz-empowered backhaul. For reliable last-mile connectivity in the end-to-end (E2E) system, non-orthogonal multiple access (NOMA) is applied with sub-6GHz spectrum. To maximize the E2E throughput, we formulate an optimization problem with diverse design variables of access and backhaul, including 3D UAV deployment, UAV transmit power, and NOMA decoding orders, with hybrid precoding and transmit power of the backhaul terminal. For this intricate problem, we propose an optimization process where the design variables are optimized sequentially. Using numerical results, we verify the feasibility of our optimization process and demonstrate supremacy of the proposed network scheme and optimization algorithm compared to other baselines. Furthermore, we corroborate design guidelines for the proposed network over access and backhaul links with various factors, such as antenna structure, the number of antennas, transmit power level, and interference.