We present and evaluate the ExaNeSt Prototype, a liquid-cooled rack prototype consisting of 256 Xilinx ZU9EG MPSoCs, 4 TBytes of DRAM, 16 TBytes of SSD, and configurable interconnection 10-Gbps hardware. We developed this testbed in 2016-2019 to validate the flexibility of FPGAs for experimenting with efficient hardware support for HPC communication among tens of thousands of processors and accelerators in the quest towards Exascale systems and beyond. We present our key design choices reagrding overall system architecture, PCBs and runtime software, and summarize insights resulting from measurement and analysis. Of particular note, our custom interconnect includes a low-cost low-latency network interface, offering user-level zero-copy RDMA, which we have tightly coupled with the ARMv8 processors in the MPSoCs. We have developed a system software runtime on top of these features, and have been able to run MPI. We have evaluated our testbed through MPI microbenchmarks, mini, and full MPI applications. Single hop, one way latency is $1.3$~$μ$s; approximately $0.47$~$μ$s out of these are attributed to network interface and the user-space library that exposes its functionality to the runtime. Latency over longer paths increases as expected, reaching $2.55$~$μ$s for a five-hop path. Bandwidth tests show that, for a single hop, link utilization reaches $82\%$ of the theoretical capacity. Microbenchmarks based on MPI collectives reveal that broadcast latency scales as expected when the number of participating ranks increases. We also implemented a custom Allreduce accelerator in the network interface, which reduces the latency of such collectives by up to $88\%$. We assess performance scaling through weak and strong scaling tests for HPCG, LAMMPS, and the miniFE mini application; for all these tests, parallelization efficiency is at least $69\%$, or better.