The reason for this specification is that Hawwa followed Adam (AS) and husbands are supposed to lead their wives and prophets are supposed to lead their followers towards good. That is why both Adam (AS)'s mistake and subsequently his repentance are emphasized, as opposed to Hawwa (AS)'s.
But, obviously, Adam and Hawwa (AS) were both forgiven without doubt. The only question is about the literary choices.
In Surah Taha, Allah says:
And they ate [DUAL] thereof, and their [DUAL] shame became clear to them; and they [DUAL] began to draw over them of the leaves of the garden; and Adam opposed his Lord, so he erred. (20:121)
Allah emphasized Adam (AS)'s error, and that is why He mentions his repentance:
Then his Lord chose him [masc. Singular], and turned towards him, and guided. (20:122)
In Surah Baqarah, for similar reasons, Allah emphasized Adam (AS)'s repentance:
Then Adam received from his Lord [some] words, and He accepted his repentance. Indeed, it is He who is the Accepting of repentance, the Merciful.
Zamakhshari comments:
He sufficed with the mention of Adam's repentance without Hawwa's repentance because she was a follower of him. [...] But, He did mention her in the verse ⟪They (both) said, "Our Lord, we have wronged ourselves⟫ (7:23)
Another reason for this emphasis on Adam (AS) is that he is the main character of the story. His wife, thus, does not usually need to be mentioned explicitly. That is why, contrary to the Bible, Allah only mentions the Shaitan tempting Adam (AS) even though it is likely he also tempted Hawwa.
And Allah knows best.
