The negation of "no friendship" and "no intercession" is general and does not mean there are no exceptions. The general case of no friendship and no intercession refers to the disbelievers. But, the exceptions of there being friendship and intercession is for the believers.
The verse claims "no friendship" but even this is is specified in other verses that the lack of friendship is only for the disbelievers and believers will have friends!
First example, Allah says:
And warn them, [O Muhammad], of the Approaching Day, when hearts are at the throats, filled [with distress]. For the wrongdoers there will be no devoted friend and no intercessor [who is] obeyed. (40:18)
Note how Allah specifies that it is for the "wrongdoers."
Second example, Allah says:
Close friends, that Day, will be enemies to each other, except for the righteous (43:67)
Here, Allah clearly specifies that the breaking of friendships is for the disbelievers and does not apply to the righteous.
As for intercession, Allah specifies in other verses that there is intercession for those who He allows. This occurs in many verses, but I will present some of them.
First example, Allah says:
None will have [power of] intercession except he who had taken from the Most Merciful a covenant. (19:87)
Secondly, Allah says:
That Day, no intercession will benefit except [that of] one to whom the Most Merciful has given permission and has accepted his word. (20:109)
Thirdly, Allah says:
And intercession does not benefit with Him except for one whom He permits. [And those wait] until, when terror is removed from their hearts, they will say [to one another], "What has your Lord said?" They will say, "The truth." And He is the Most High, the Grand. (34:23)
These verses all clearly mention that intercession can occur with Allah's permission. If it was correct to interpret the earlier verse as meaning no intercession ever at all, this would not make sense to say.
Fourthly, Allah says referring to the disbelievers:
So there will not benefit them the intercession of [any] intercessors. (74:48)
This verse is very interesting because it affirms the existence of "intercessors" then negates their intercession affecting these disbelievers!
How do these verses combine with the verse that says "no intercession"?
We could combine them in two ways: 1) what I first mentioned that the original verse is a general statement that does not negate the existence of exceptions, and 2) the original verse means "no intercession against Allah's permission" rather than intercession in general.
The ahadith and statements of the Prophet (SAW) affirming the existence of intercession are also too numerous to count. They might even be called mutawatir (mass-transmitted) similar to the Quran. So, it is not simple to just deny them like that.
Do not be confused with your understanding of a verse contradicting a hadith with the verse itself truly contradicting a hadith. You need to line up your understanding of verses with the ahadith, and the ahadith don't need to bend in your favor.
And Allah knows best.