Is the succession on Earth for the believer alone, or for humanity in general?

Succession (Khilafah) is originally for the believers who act righteously and are just, as Allah Almighty described them in His saying: "And Allah will surely support those who support Him. Indeed, Allah is Powerful and Exalted in Might. Those who, if We establish them in the land, will establish prayer and give zakah and enjoin what is right and forbid what is wrong." (Quran 22:40-41) And His saying: "Allah has promised those among you who have believed and done righteous deeds that He will surely grant them succession [to authority] upon the earth just as He granted it to those before them." (Quran 24:55) As for His saying, the Almighty: "Indeed, I will place upon the earth a successor," (Quran 2:30) what is meant by it are generations that succeed one another, starting with Adam and his progeny, as Allah Almighty said: "It is He who has made you successors upon the earth." (Quran 6:165)