Is the companion who sought forgiveness upon hearing an invocation against someone who had burned the Qur'an considered an infidel due to not being affected or due to his approval of the act? And what is the duty in this situation?

A person's mere seeking of forgiveness does not necessarily expiate their sin, as it is possible they are not pleased with what occurred. And if there are ninety-nine reasons to declare a Muslim an unbeliever and one reason to keep them within Islam, then one should act upon that single reason, relying on the Prophet's (peace be upon him) saying: "Avert the prescribed punishments from Muslims as much as you can." What is obligatory is to gain deep understanding of Tawhid (monotheism) and what contradicts it, and for Muslims to strive to support their religion, invite to it, and defend it.