What form of worship was manifested from the incident of Adam (alayhissalam) and Shaytan?

The names of Allah; Al-Ghafir, Al-Ghaffar and Al-Ghafur, all come from a root ghfr which means to cover. Relative to Allah, it means He is the one who covers sins and blots out sins, whether it is due to our repentance or whether it is due to other factors like the righteous deeds that we might do.

The concept of repentance is pleasing to Allah. This is what differentiated Satan and Adam. Both of them sinned; Satan sinned when he refused to bow to Adam and Adam sinned when he ate from the forbidden tree. What made the difference between them that Adam became blessed as a Prophet while Satan became cursed till the last day? The difference was; Adam turned back to God in repentance while Satan became more arrogant and proud.

Allah loves to forgive His slaves, more so even, as the example given by Prophet Muhammad (ﷺ), than a person who finds his camel after losing it in the desert. He finds it after giving up all hope, finds it laden with goods and he is so happy, Allah is even happier with one who turns back to Him in repentance.

Repentance is a powerful form of worship of Allah, which Allah wants from us. It is our means of purifying ourselves from sin. No one can do this but us; we have to turn to Allah.