Why was Waraqah ibn Nawfal not the first to embrace Islam after his glad tidings to the Prophet (peace and blessings be upon him) regarding the prophethood? And did he embrace Islam, and when? And what is the source of this information?

Waraqa ibn Nawfal was one of four individuals who agreed upon the deviation of Quraysh from the religion of Abraham. Waraqa converted to Christianity and read the scriptures of ancient peoples. When the Prophet (peace be upon him) came to him after the revelation, Waraqa confirmed to him that he was the prophet of this nation, and that what came to him was the Great Namus (Gabriel), who had come to Moses. Waraqa died before the advent of Islam. The Prophet (peace be upon him) saw him in a dream wearing white clothes and said: "I saw for Waraqa a garden, or two gardens."