Is it possible for one to uphold justice with all of humanity, considering that the Qur’an indicates the inability to be just with a wife, and given the questioner’s feeling of shortcoming in their worship?

A Muslim must strive to achieve justice in all aspects of their life, to the best of their ability. For justice is what the heavens and the earth were established upon, and it is among the greatest things Allah has commanded. Allah Almighty has commanded justice and ihsan (excellence), and to render trusts to their rightful owners, and when you judge between people, to judge with justice. Absolute justice is an attribute of none but Allah, Glorified and Exalted be He. Therefore, hardship has been removed concerning what is beyond one's capacity and ability in fulfilling weights and measures, for "We do not burden a soul beyond its capacity." As for the mentioned hadith, "Love for people what you love for yourself, you will be the most just of people," it has no authentic chain of transmission; it is fabricated. The authentic hadith suffices in its place: "None of you truly believes until he loves for his brother what he loves for himself."