Zuko's complexity makes him so interesting in these fanfictions. He has a troubled past which has shaped him, but he is constantly evolving. His ability to show vulnerability in front of the reader is another great trait. It allows for a deeper emotional connection between him and the reader, as seen in stories where he opens up about his insecurities and fears.
His friends would probably take care of him. Midoriya would be very eager to help, using his kind-hearted nature. He would make sure Todoroki is fed and comfortable.
One idea could be that all his friends at UA plan a surprise birthday party for him. They decorate the common room with his favorite colors, blue and red. Another plot could be Todoroki spending his birthday with his family, trying to reconcile with his father on this special day. Maybe he receives a heartfelt gift from his mother that has a deep emotional significance.
Todoroki's character development in time travel fanfictions can be quite profound. He may start as a somewhat aloof character, but through time travel, he begins to understand the importance of relationships more deeply. When he travels back and witnesses the relationships he could have had or lost, it makes him cherish the ones he has in his original timeline. His view of heroism also evolves. He realizes that being a hero isn't just about using his powers but also about making the right choices at the right time, which is especially highlighted when he has to make decisions that could change entire timelines.
In 'Ozai Hurts Zuko' fanfictions, Zuko develops by facing his inner demons. The harm from Ozai makes him re - evaluate his life. He might become more empathetic towards others who have suffered, and this changes his outlook on the world. He also gains a new sense of self - identity, separate from what his father wanted him to be.