How authentic is the narrated Hadith which mentions that the Companions Abu Bakr, Umar, Uthman, and Ali mentioned what they loved from this world after the Prophet's saying, "From your worldly life, women and perfume have been made beloved to me, and the coolness of my eyes has been made in prayer"?

The Hadith: "From your world, women and perfume have been made beloved to me, and the coolness of my eyes has been placed in prayer," is authentic, narrated by Ahmad, An-Nasa'i, and others.

As for what was attributed to the Rightly Guided Caliphs afterwards, it is not found in the books of Hadith. Rather, Al-Ajlouni mentioned it in "Kashf Al-Khafa'" quoting from "Al-Mawahib" with the wording: When the Prophet, peace and blessings be upon him, said that, Abu Bakr said: Three things have been made beloved to me: looking at your face, collecting wealth to spend on you, and seeking intercession through your relatives. And Umar said: Three things have been made beloved to me: enjoining good, forbidding evil, and upholding Allah's command. And Uthman said: Three things have been made beloved to me: feeding the hungry, quenching the thirsty, and clothing the naked. And Ali said: Three things have been made beloved to me: fasting in summer, hosting guests, and striking with the sword before you.

That is weak and not found in the relied-upon books of Hadith.