First question is what do you mean by STM32? The Adafruit code runs on most Arduinos including STM32. But again you say no Arduino, so no idea of what underlying software you might be using.
Some of the main differences from adafruits driver to the _t3 (or my _t3n) is that ours have been optimized to work with the T3 and T4 hardware... So I am not sure what you would gain by using it.
Obviously if you were to say that you have a lot of T3.x boards and need to port your code over than it might make some sense.