So 994 (and the years around it) would have actually been a pretty interesting time for our Sasanian traveller to visit. Mesopotamia wasn't actually ruled by the Abbasid caliphs but rather by the Buyids, a Pahlavi-speaking, ethnically Iranian Dailamite group of Shia Muslims. Although they weren't very successful at it, they also made a serious effort around this time to present themselves as a Persian monarchy, so that in 994, in the midst of a succession struggle, the two Buyid rulers (one based in Mesopotamia, the other in Iran) were both referring to themselves as "Shahinshah" and issuing coinage depicting themselves as classical Persian royalty.

That being said, it's unlikely that, beyond these superficial trappings, that you would have seen much in terms of administration that would have reminded you of 394. The military autocracy, while led by the Iranian Buyids, would also have prominently included Turks and Kurds. The legal system would have been a mix of religious law and autocratic decrees issued by a mix of mercenary and quasi-feudal rulers who for much of this period exercised a significant degree of independence from central authority. While the Zoroastrian fire temples still burned in Iran, in Mesopotamia these would have been gone and instead the religious landscape would have been dominated by Islam.

Islam is very much a religion of public spaces so this would have been quite obvious to you. Aside from the five daily calls to prayer and the visible minarets throughout your city (which would likely have been the tallest structures around) mosques and their environs would have been a major social hub of the society for communal gatherings, leisure, education and trade.

While Persian/Pahlavi would have had a strong presence, in Mesopotamia the population would have also been strongly Arabized, particularly in the South with cities like Basra and Kufa. Arabic script dominated even when the language itself was Persian. While the Buyid rulers may have produced coins depicting themselves as Sassanian-esque Persian royalty, the dress, language, and social norms in Mesopotamia would have been almost entirely Arabized and Islamized, Mesopotamia having seen extensive Arab colonization efforts and having been one of the earliest regions to become majority Islamic.

Sources: See The Cambridge History of Iran volume 4, "Iran Under the Buyids"

and The Venture of Islam by Marshall Hodgson which goes into more details than I'd be able to remember off hand about social structures and conventions, day-to-day administration and other topics about how Islam would have functioned in the period.