WELCOME i'm laura, and i'm super excited for jessica, although admittedly i have never watched jj and my familiarity with the character begins and ends entirely with her comics counterpart...

—but speaking of, idk if you're familiar with the comics at all, but peter does know jessica and she's one of the increasingly not-few people who are aware that he's spider-man. however! peter's also intensely familiar with the multiverse and won't be overly shocked to encounter a jessica who doesn't know who he is, as an obvious by-the-by.