According to dictionaries, we can call a character in a book or a movie “sympathetic” to mean they are relatable or likable. For example, “Harry Potter is a sympathetic character.” What I wonder about is, can we call a real person instead of a character “sympathetic” to mean they are relatable/likable, or do I have to use it with that meaning only if I am talking about a fictional character? For example, let’s say I am watching a documentary about a real person who has social anxiety and I find him relatable because I have social anxiety too and I feel a connection with him. Can I say, “He is a sympathetic person” or “He is sympathetic”? Or let’s say I feel a connection with a friend of mine, can I say, “He is sympathetic”?
You can most certainly describe a real person as sympathetic, and that is often how it is used. It is usually describes someone who is able to show concern for someone in a bad situations. It is sometimes also used to describe someone who is likeable or pleasant.
Saying that someone is sympathetic because you can relate to someone isn't really how you would use the word usually. You may be sympathetic if you show concern for someone else who is struggling, but saying they are sympathetic for you being able to relate to them is not the same.
You may also be thinking of the word empathetic. This means that you're able to put yourself in someone else's shoes. You are easily able to relate to them. This may be the word that fits this situation a little better.
Let's say you're in a situation where your friend is dealing with a breakup. If you felt sorry for him and his bad situation,you would be sympathetic. He wouldn't be sympathetic for you feeling sorry for him. But, in a separate situation, he may be sympathetic or have a sympathetic character if he is a likeable or pleasant person.