Got it in one: they think Dany doesn’t speak Valyrian (which is partly why the Astapori think of her as a barbarian, because anyone who’s civilized speaks it), so Missandei is there to translate.
High Valyrian is pretty clearly modelled on previous international languages, but in slightly weird ways. On the one hand, because it’s the language of classical scholarship, it’s taught in the Citadel, and educated highborn people like Tyrion learn it as part of being cultured, it’s a lot like how Latin was the international language of the literate in Medieval and Early Modern Europe.
And it’s also got that root-language thing; in the same way that Latin gave rise to the Romance languages, High Valyrian has given rise to the dialects of the Free Cities. Thus, Kraznys doesn’t speak particularly good Valyrian, “twisted and thickened by the characteristic growl of Ghis, and flavored here and there with words of slaver argot.” Grazdan is probably better-educated than Kraznys; hence being able to speak Westerosi (although not well), so his Valyrian is better.
On the other hand, trade languages aren’t usually the grammatically complex, sophisticated languages of scholarship. They tend to be simplified pidgins, because they’re being used in inter-cultural communication and you’re primarily interested in buying and selling and things like complex declensions and cases and tenses just get in the way of business. So for example, the original linga franca which emerged in the Mediterranean in the medieval period, used a simplified Italian as its base because of the prominence of Italian merchants, and then added on large numbers of loan words from almost every language group a merchant might encounter in the Mediterranean, from Spanish and French to Turkish.