I just watched the episode. The writing on this show continues to be so bad.
For example, it felt so strange to see Burnham's over-the-top celebration when she learned that there are other people around. It's like the writers are using her mixed heritage (a Human who was raised on Vulcan) as an excuse to have her act like the most calculating, logical Vulcan in some situations and the most emotional, irrational Human in others. There's no consistency like there was with Spock (Nimoy's Spock).
Also, later, the guy activates a cloaking device on his cargo and Burnham, as if she's being clever, deduces out loud that he doesn't want anyone else to find it. Shortly after, she acts shocked and saddened that the Federation is gone and even says "that's impossible," even though she went
900 years into the future. What did she expect? That's like expecting the Knights Templar to still be active today. Then, after hearing some more, she repeats "that's not possible" and exposits for the audience's sake that the Federation is not about ships and warp drives, but about a vision and all those who believe in that vision

. Speaking of which, it's so nice to have a character soapboxing about Starfleet values after she was given a life sentence for mutiny.