In-band full duplex cell-free (CF) systems suffer from severe self-interference and cross-link interference, especially when CF systems are operated in distributed way. To this end, we propose the multicarrier-division duplex as an enabler for achieving full-duplex operation in the distributed CF massive MIMO systems, where downlink and uplink transmissions occur simultaneously in the same frequency band but on the mutually orthogonal subcarriers. To maximize the spectral-efficiency (SE), we introduce a heterogeneous graph neural network (HGNN) specific for CF systems, referred to as CF-HGNN, to optimize the power-allocation (PA). We design the adaptive node embedding layer for CF-HGNN to be scalable to the various numbers of access points (APs), mobile stations (MSs) and subcarriers. The attention mechanism of CF-HGNN enables individual AP/MS nodes to aggregate information from the interfering and communication paths with different priorities. For comparison, we propose a quadratic transform and successive convex approximation (QT-SCA) algorithm to solve the PA problem in classic way. Numerical results show that CF-HGNN is capable of achieving 99\% of the SE achievable by QT-SCA but using only $10^{-4}$ times of its operation time. CF-HGNN significantly outperforms the traditional greedy unfair method in terms of SE performance. Furthermore, CF-HGNN exhibits good scalability to the CF networks with various numbers of nodes and subcarriers, and also to the large-scale CF networks when assisted by user clustering.