Would writing about how my background has shaped me into who I am today (e.g. differences in mindset in Americans vs other cultures) and how it also has influenced my interest in linguistics be an effective way for me to share who I am as a person?
I think that sounds like an interesting topic, in that you are tying race/ethnicity into your interest in linguistics and talking about how it has shaped you. The essay should give the reader a sense of who you are and why you would be an interesting and valuable addition to the school community. People often warn against writing something too stereotypical or too much along the lines of “what I have overcome to get where I am today,” but as you describe your topic, that isn’t how it sounds. My son, who has a complex ethnic and cultural background, write about that in his essay, and he had good success with his applications. His tone was light, but he explained how having insight into a range of cultures had shaped him and how he expects to take advantage of that in the future.