In The Lord of the Rings: The Rings of Power S01E08 "Alloyed", Sauron* has revealed himself to Galadriel and says to her:

* in the form of Halbrand

Sauron (speaking in the form of Finrod in a vision to Galadriel): My task was to ensure peace. But I learned that was Sauron's task as well.
[...]
He was seeking a power not to destroy Middle-earth, but to heal it. Just as your fellow Elves are seeking to do this very moment.

Sauron: When Morgoth was defeated, it was as if a great, clenched fist had released its grasp from my neck. And in the stillness of that first sunrise, at last, I felt the light of The One again.
And I knew if ever I was to be forgiven... That I had to heal everything that I had helped ruin.

Galadriel: No penance could ever erase the evil you have done.

^{- The Lord of the Rings: The Rings of Power S01E08 "Alloyed" (emphasis mine)}

Was this just an attempt to deceive Galadriel? Or was Sauron, at that point, truly sorry and was seeking forgiveness for what he had done under the service of Morgoth? In the books, did Sauron, at one point, show the same motivation for his actions?