Zuko doubts himself because of his trauma and upbringing, but he actually is a very well-liked fire lord, especially among international circles. His earnest desire to right the wrongs of the past and down-to-earth, humble demeanor is seen as endearing by other nations' diplomats and leaders.
He also gets along well with palace staff, as he's very gracious to them, and talks to them like a regular person, and remembers their spouses' and children's names. Ordinary citizens take a liking to him because of this and his kind personality.
What helps Zuko a lot in this is that he's actually very good at reading people and anticipating their needs. He is proactive and acts before they ask, seeing ahead in how things could impact them. Zuko is very empathetic, and this helps him a lot in everyday conversations as well as political ones.
Zuko worries constantly that he's unlikeable as both "just a person", as "just Zuko", and as the fire lord and how that it impacts how he can help people and the world's peace. But others don't see him that way at all. His anxiety, abuse, and trauma all impact how he clearly can see himself and his successes and strengths.
He became very good at reading people likely the same way Azula did. It was a survival mechanism where they had to watch Ozai's every move closely to anticipate how to behave to stay afloat. It also helped him monitor how Ozai might lash out against their mother as well. Azula took reading people in order to better serve her father by manipulating them to her whim, whereas Zuko's empathy made him work better this way to be a considerate and effective world leader.
