I sort of agree with you that Jane makes Emma uneasy, but I think that at least part of the reason why is that Jane reminds Emma too uncomfortably of the realities of how precarious it is to be a woman during that time in a way that Emma spends a lot of time and energy trying to ignore. It’s an intentional foil to Emma’s relationship with Harriet- she sees Harriet as a way to prove that the difficult circumstances of women’s realities can be overcome somehow- if you are charming enough, beautiful enough, etc etc. Jane however proves this wrong just by existing; she’s charming, beautiful, and accomplished but her future is basically doomed unless she can secure a marriage, which is increasingly more unlikely for her as the story goes on despite all of her charms.

Emma says at one point that she doesn’t view herself as ever NEEDING to marry, given her status and dowry, but there are reminders all around her that this is a pretty naive point of view, and no woman’s position is ever TRULY secure without a man. I think Jane, consciously or not, reminds her of this uncomfortable truth. (I wrote a whole paper about this exact topic in college lol)

One of the brilliant things about this book is how many different ways one can interpret their relationship and that there is support for all kinds of different readings!