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Microwave Kinetic Inductance Detectors (MKIDs) are superconducting detectors capable of single-photon counting with energy resolution across the ultraviolet, optical, and infrared (UVOIR) spectrum with microsecond timing precision. MKIDs are also multiplexable, providing a feasible way to create large-format, cryogenic arrays for sensitive imaging applications in biology, astronomy, and quantum information. Building large, cryogenic MKID arrays requires processing highly multiplexed, wideband readout signals in real time; this task has previously required large, heavy, and power-intensive custom electronics. In this work, we present the third-generation UVOIR MKID readout system (Gen3), which is capable of reading out twice as many detectors with an order of magnitude lower power, weight, volume, and cost-per-pixel as compared to the previous system. Gen3 leverages the Xilinx RFSoC4x2 platform to read out 2048, 1 MHz MKID channels per board. The system takes a modern approach to FPGA design using Vitis High-Level Synthesis to specify signal processing blocks in C/C++, Vivado ML intelligent design runs to inform implementation strategy and close timing, and Python productivity for Zynq to simplify interacting with and programming the FPGA using Python. This design suite and tool flow allows general users to contribute to and maintain the design and positions Gen3 to rapidly migrate to future platforms as they become available. In this work, we describe the system requirements, design, and implementation. We also provide performance characterization details and show that the system achieves detector-limited resolving power in the case of few readout tones and minimal degradation with all 2048 tones. Planned upgrades and future work are also discussed. The Gen3 MKID readout system is fully open-source and is expected to facilitate future array scaling to megapixel-sized formats and increase the feasibility of deploying UVOIR MKIDs in space., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)