”The last recorded exploration was over a century before Doctor Vellek was even born.” That does potentially raise the question of how Burnham would have been so familiar with Lyrek in the previous episode, though of course she and most of the rest of the Discovery crew might have been alive before Doctor Vellek’s birth.
We've seen that in her one year as a courier, Burnham learned everything about every planet because of secret criminal space knowledge. Even if the last recorded exploration was that old, presumably space pirates with their gritty streetsmart know-how have some sort of Mos Eisley medieval market nearby.
What a bizarre three ships to start with