Is the Hadith that states that abandoning one's homeland and emigrating to another country indicates a deficiency in faith authentic?

We have not come across anything that suggests that love of one's homeland is part of faith, apart from the popular saying "Love of one's homeland is part of faith," which is a fabricated hadith. Al-Albani mentioned that the meaning of this hadith is not sound, because love of one's homeland is an innate human instinct, and one is not praised for it; all people share this love, their believers and disbelievers alike. As for a person residing in their homeland or leaving it, both are originally permissible, unless there is an impediment, or one is favored over the other by a preponderant factor.