This work presents the first silicon-validated dedicated EGM-to-ECG (G2C) processor, dubbed e-G2C, featuring continuous lightweight anomaly detection, event-driven coarse/precise conversion, and on-chip adaptation. e-G2C utilizes neural network (NN) based G2C conversion and integrates 1) an architecture supporting anomaly detection and coarse/precise conversion via time multiplexing to balance the effectiveness and power, 2) an algorithm-hardware co-designed vector-wise sparsity resulting in a 1.6-1.7$\times$ speedup, 3) hybrid dataflows for enhancing near 100% utilization for normal/depth-wise(DW)/point-wise(PW) convolutions (Convs), and 4) an on-chip detection threshold adaptation engine for continuous effectiveness. The achieved 0.14-8.31 $μ$J/inference energy efficiency outperforms prior arts under similar complexity, promising real-time detection/conversion and possibly life-critical interventions