Or HaChaim on Genesis 21:3/אור החיים על בראשית כ״א:ג׳

1 בנו הנולד לו, His son who had been born to him. Inasmuch as Abraham had another son, Ishmael, the Torah records here that Abraham stressed that this was the son who was fit to bear his name and who would fulfil the aspirations he had for him. No such comment is recorded at the time Ishmael was born. The Torah's addition אשר ילדה לו שרה, whom Sarah bore for him, is an allusion to the fact that both had constantly prayed. Abraham had asked that all his descendants should be issue of his righteous wife Sarah, whereas Sarah had also prayed to be the mother of all of Abraham's children. The word שרה refers to her prayer, whereas the words אשר ילדה לו, refer to Abraham's prayer.

2Another reason for this nuance is that the name יצחק, i.e. joy, reflects the fact that an old woman had given a son to an old man. Sarah spelled this out in greater detail in verse 6.