Aquinas simply isn’t altogether relevant to many of the non-Latin traditions, not because he is wrong, but because he’s entrenched in a theological framework that is peculiarily Latin. Most traditions have their own way of asking questions, and of approaching the mysteries of God; some are quite compatible with Aquinas, others aren’t. This is true, in fact, even within the Latin context; Franciscan spirituality, for example, really doesn’t owe much to Aquinas’ approach, and wouldn’t depend much on him.
Ironically the mystical elements of the Latin tradition, especially the Carmelites, owe a lot to Aquinas’ theology. His strong emphasis on Realism, and therefore on REAL participation in Divinity for a very solid basis for the mystical experiences of prayer and the Sacraments. For Aquinas, when we receive Sanctifying Grace we are not merely being uplifted within our own nature, we are actually sharing in God directly; our nature remains human, but is modified by a Divine addition, and Divine powers actually become part of our soul (the theological virtue of Charity, for example, is literally a share in the Divine Love according to Aquinas; we no longer love with the power of human nature, we love with the power of the Divine Nature as humans). This emphasis had a profound impact on the writings of Latin mystics like St. John of the Cross, who was unapologetically Thomistic (in the broad, non-Banezian sense) in his theology.
Peace and God bless!