In ordinary Urdu, an “ʿazīz friend” means a dear friend. But in khabar ʿazīz, the label concerns narrator numbers.
In the Hadith about love for the Prophet ﷺ, keep two points distinct:
• The saying's meaning: placing love for the Prophet ﷺ before love for all other people.
• Why it is called ʿazīz: no generation has fewer than two narrators.