Is walking to the mosque rewarded, and does the Noble Verse: "And We record that which they have put forth and what they have left behind [their traces]" have a connection to that, such that the angels record the steps of the worshiper to the mosque?

Walking to the mosque is encouraged in the Sunnah of the Prophet, and the Prophet, peace and blessings be upon him, gave glad tidings to those who walk to the mosques in darkness of complete light on the Day of Resurrection. The interpretation of His saying, "And We record what they have put forth and their traces," includes the footsteps of a servant towards obedience or disobedience, and that Allah enumerates every trace and deed of a human being. There are hadiths that affirm this meaning regarding the virtue of walking to prayer, and the angels record the good deeds of humans and others.