Praise be to Allah, and may peace and blessings be upon the Messenger of Allah. To proceed:
There is no contradiction between the verses of the Qur’an, because the Qur’an is the Word of Allah تعالى. He says:
“Do they not reflect deeply upon the Qur’an? Had it been from anyone other than Allah, they would surely have found in it much contradiction.” [An-Nisa’: 82]
The way to reconcile the verses is that the intercession that is denied is intercession for the disbelievers, or intercession that takes place without the permission of Allah تعالى. As for the intercession that is affirmed, it is the intercession which Allah permits and in which He is pleased with both the intercessor and the one for whom intercession is made.
Allah تعالى says:
“Say: To Allah belongs all intercession.” [Az-Zumar: 44]
And He says:
“Who is it that can intercede with Him except by His permission?” [Al-Baqarah: 255]
Regarding the affirmed intercession, Allah تعالى says:
“On that Day, intercession will not benefit except for one whom the Most Merciful has permitted and whose word He is pleased with.” [Ta-Ha: 109]
And He says:
“And they do not intercede except for one with whom He is pleased.” [Al-Anbiya’: 28]
Thus, Allah تعالى is the sole Owner of all intercession. None of creation possesses the independent ability to intercede. Rather, Allah سبحانه permits whomever He wills among His prophets, angels, and righteous servants to intercede, and He is pleased with both the intercessor and the one for whom intercession is made.
As for the disbelievers, intercession will not benefit them. Allah تعالى says:
“So the intercession of the intercessors will not benefit them.” [Al-Muddaththir: 48]
Therefore, the verses that deny intercession are understood as referring to the intercession that is denied by Islamic law: intercession for the disbelievers or intercession without the permission of Allah. As for the intercession which Allah has permitted, it is affirmed by the Qur’an and the Sunnah.
The exception mentioned in the Sunnah is the Prophet’s ﷺ intercession for his uncle Abu Talib in having his punishment lightened, not in bringing him out of Hellfire.
And Allah تعالى knows best.