The first sentence could be rephrased as: "Born into a wealthy family, Haru Jigokumeguri radiates beauty and intellect as the eldest daughter of a successful businessman."
For the second sentence, a possible rewrite is: "In contrast, Kawayanagi Tsurezure dresses in vintage attire and delights in gazing skyward for extended periods, making him an uncommon character."
Instead of "Contrarily," we could use "However" or "Nevertheless" to link the two characters' descriptions.
To rephrase "Although Haru is prideful and egotistic, she struggles to connect with others," we could say: "Despite her prideful and egotistic demeanor, Haru finds it challenging to form meaningful connections with others."
The next sentence could be written as: "Likewise, Kawayanagi's difficulty in socializing creates obstacles for effective communication between him and Haru."
A possible rewording of "As social pariahs, the two forge an unanticipated bond" is: "Despite their status as social outcasts, they form an unexpected bond."
Finally, we could revise "Their mutual friend, Akane Tendou, brings happiness into their companionship, motivating the duo to overcome their insecurities and focusing on individual enhancements" as: "Through their mutual friend Akane Tendou, they discover joy in each other's company, inspiring them to confront their insecurities and strive for personal growth."