You don't have to marry a Polish person. What if you participated in more Polish cultural events? Meet some local Poles, take some Polish language classes. It feels like there are plenty of low-barrier things that you could do to help you reconnect with that part of your heritage if it bothers you enough.
As for the article, I'm willing to believe that her fear of missing her connection to her culture is merely a manifestation of her grief at losing her mother. Otherwise, it would sound more like she's a little sad, but not enough to do anything about it. Certainly her call either way, but the latter would make me sad that it made its way into the New Yorker.