Is a law student—who is studying a major they dislike and is suffering from the hardship of studying and being far from the university—considered a طالب علم (seeker of knowledge) who will be rewarded for their efforts, or does the Hadith "Whoever traverses a path seeking knowledge..." apply only to the seeker of religious knowledge, thus rendering their studies devoid of any worldly or otherworldly value or reward?

What you have understood is incorrect. You can earn immense reward by continuing your studies with the intention of honoring your parents, benefiting Muslims, defending the innocent, restoring the rights of the oppressed, and being a role model for committed youth. All of these are righteous intentions for which you will be rewarded, and your studies will become an act of closeness to Allah. We advise you to cast aside these delusions and strive diligently in your studies, combining the interests of your religion and your worldly life, while mindful of good intentions.