Does mentioning what was stated in a Hadith about the attitudes of a person who does not accept advice, with the intention of seeking guidance from another person on how to deal with him, constitute backbiting, knowing that the intention was not to mention the person's faults but to refer to situations that occurred from him?

Backbiting is mentioning a Muslim with what he dislikes. Therefore, if a person dislikes the mention of a stance he took, then this is forbidden backbiting, and it is not permissible to mention it to another person, even if it is to seek guidance on how to deal with him. Backbiting is not permissible except for specific and well-known reasons.