Why is loving the Prophet (ﷺ) an essential part of Islamic faith?

The basis of loving the messenger of Allah (ﷺ) is a statement quoted by Abu Muhammad, 'Abdullah bin Amr bin al-'As (رضى الله عنه) reported that the Messenger of Allah (ﷺ) said:

"None of you (truly) believes until his desire or inclination is in accordance with what I have brought or subservient to what I came with."[1]

This statement explains that faith depends on our love for the prophet (ﷺ). Loving him is an essential part of faith. This is also reinforced by the fact comprised of two statements, “there is no one worthy of worship but Allah and Muhammad (SAW) is the messenger of Allah.” We repeat it in Salah and is a means of entering Islam, mentioned in Qur'an and the statement of the Prophet (ﷺ).

Reference:

[1] [A fine and genuine hadith which was related by al-Maqdidsi in his Book of Hujjah, An-Nisaa’ee and Bukhari, Muslims]