Bucky’s first arc started in Civil War, of course, and continued through Endgame: A broken, enslaved super-soldier saved several times by his friend Steve Rogers and aided by Wakandan technology. By the time of TFAWS, he’s got PTSD, he’s looking for redemption. He’s befriended the father of one of his victims but Bucky’s stuck, he’s unable to follow through on what would help him (and Mr. Nakajima) move on. Existentially unsure of his purpose, he’s socially isolated. So Bucky’s second arc — across TFAWS — is one of finding purpose, finding new friendship after his only friend (Cap) “died,” and making amends to the people on his list. A redemption arc. That’s his journey, but his new friend Sam Wilson needs his help accepting his destiny as the new Cap and his help in literal terms to complete the missions that will get him there.