Why did Allah not forgive Satan for his sin, despite the immensity of His mercy, while He forgives whom He wills for sins other than shirk (associating partners with God)?

Iblis did not repent or seek forgiveness from his Lord; rather, he insisted on his arrogance and disobedience. This is in contrast to Adam (peace be upon him), who repented and sought forgiveness from his Lord.

After learning of Allah's wrath upon him, Iblis requested respite not for repentance, but to mislead the Children of Adam.

Adam's sin was due to desire, and he repented. As for Iblis's sin, it was due to arrogance and pride, and he did not repent.

Allah accepts the repentance of the penitent, no matter how great their sins, and His mercy is vast.

No one enters Paradise by their deeds, but rather by Allah's mercy and grace. Good deeds are a means to attain Allah's mercy and to elevate one's ranks in Paradise.