Drift chambers have long been central to collider tracking, but future machines like a Higgs factory motivate higher granularity and cluster counting for particle ID, posing new data processing challenges. Machine learning (ML) at the "edge", or in cell-level readout, can dramatically reduce the off-detector data rate for high-granularity drift chambers by performing cluster counting at-source. We present machine learning algorithms for cluster counting in real-time readout of future drift chambers. These algorithms outperform traditional derivative-based techniques based on achievable pion-kaon separation. When synthesized to FPGA resources, they can achieve latencies consistent with real-time operation in a future Higgs factory scenario, thus advancing both R&D for future collider detectors as well as hardware-based ML for edge applications in high energy physics.