How should one deal with a friend who was upon the methodology of Ahl al-Sunnah, then embraced Ash'ari thought, and began praising certain Sufi domains, and denying the torment of the grave, while refusing advice and merely stating that the response is found in Ash'ari and Sufi books? And is conveying the conversation that took place between the questioner and this friend to other friends, with the intention of complaining, warning, or grumbling, considered backbiting?

You should advise your friend to read books of the Salaf concerning creed, and those that criticize Ash'arism and Sufism. It is astonishing that he denies the torment of the grave while embracing Ash'arism and Sufism, which indicates his confusion regarding the matter. The general rule is that boycotting a Muslim is forbidden, except for a legitimate Shar'i benefit, such as when the innovator or the open sinner is deterred by the boycott, or when the number of those deceived by him decreases. So, boycotting for a religious benefit is permissible. However, if there is no fear of harm and no benefit is achieved from the boycott, then it should not be initiated. May Allah benefit him through your companionship. Boycotting differs depending on the time, place, and type of innovation. It is permissible to mention his situation to someone whose help is sought in denouncing and advising, and for warning against him if he persists in his innovation and there is fear for others. This is an exception from forbidden backbiting for a legitimate Shar'i purpose.