Following the scale-up of new radio (NR) complexity in 5G and beyond, the physical layer's computing load on base stations is increasing under a strictly constrained latency and power budget; base stations must process > 20-Gb/s uplink wireless data rate on the fly, in < 10 W. At the same time, the programmability and reconfigurability of base station components are the key requirements; it reduces the time and cost of new networks' deployment, it lowers the acceptance threshold for industry players to enter the market, and it ensures return on investments in a fast-paced evolution of standards. In this article, we present the design of a many-core cluster for 5G and beyond base station processing. Our design features 1024, streamlined RISC-V cores with domain-specific FP extensions, and 4-MiB shared memory. It provides the necessary computational capabilities for software-defined processing of the lower physical layer of 5G physical uplink shared channel (PUSCH), satisfying high-end throughput requirements (66 Gb/s for a transition time interval (TTI), 9.4-302 Gb/s depending on the processing stage). The throughput metrics for the implemented functions are ten times higher than in state-of-the-art (SoTA) application-specific instruction processors (ASIPs). The energy efficiency on key NR kernels (2-41 Gb/s/W), measured at 800 MHz, 25 °C, and 0.8 V, on a placed and routed instance in 12-nm CMOS technology, is competitive with SoTA architectures. The PUSCH processing runs end-to-end on a single cluster in 1.7 ms, at <6-W average power consumption, achieving 12 Gb/s/W.