Are the reasons behind the legislation of each salah authentic?

Assalamualaikum wa rahmatullahi wa barakatuh, It has been said that each prayer has a specific hikmah behind it. For instance, it has been said that for fajr, it was because Adam عليه السلام saw darkness and became afraid and so prayed a rak’at due to fear, and when it became light he prayed another rak’at due to gratefulness — and this became Fajr. (Source: https://www.islamweb.net/ar/library/content/307/1937/باب-الصلاة-الوسطى-أي-الصلوات-هي-) Is this true? JazakAllah khair