How fully incorporated was Afghanistan into the Islamic world, and how directly was it ruled from Baghdad?
Very autonomous. Unlike western Persia which fell under direct Arab control, the Parthian/Persian nobles of Eastern Persia survived relatively unscathed and in control of their lands, being nominally Muslim and under the Caliphate, they ruled the lands for the Caliphate like they had done for centuries under the Sassanid empire, after the Caliphate weakened these same nobles were the first ones to break free and form independent realms like the Samanids, Safarids, Tahirids etc.