It’s interesting to see Steve’s insecurity about his friendship with Bucky. Bucky was his best friend, and presumably his only friend. Steve idolized him. As he told Natasha and Sam: even when he had nothing, he had Bucky.
But Bucky? Bucky had a family – parents, probably some siblings. He likely had friends from school, work friends, and friends from army training. He had endless girlfriends. We know he was popular. Bucky had an entire life, and objectively, Steve was only a part of it.
Before Captain America, Bucky was Steve’s world, but Steve may not have been Bucky’s. And because of that, you can see Steve constantly second guess Bucky’s love for him. During CATFA, he doesn’t know if Bucky will follow him into war. In the CATWS funeral flashback, he doesn’t want to intrude on Bucky’s life (even though if the situation were reversed, you know he’d never let Bucky ‘get by on his own’). Even during the final CATWS fight scene, he says ‘You’re my friend’ instead of ‘We were friends’. He’s horrified that Bucky died following him, because Bucky had a life outside of Steve.
I don’t think Steve realized how important he is to Bucky until he broke the Soldier’s programming, just by existing.