That means men and women shouldnt be alone in private places.

Okay so why does it say:

Whoever has faith in Allah and the Last Day, let him not be alone with an unrelated woman without her guardian.

The emphasis on the guardian is important. That means that a sister needs to have a guardian with her whenever possible for a man to be with her, in the sense of how a man who is with a non-mehram in a public area shouldn't be. Let's take, for example, a sister who goes to the book store with her mehram. Her mehram then goes to the bathroom, and a non-mehram brother approaches her. They talk alone for a long period of time then as her mehram is returning, the brother leaves. Do you not see a problem with this where a sister with an appropriate chaperone is in a public area, but as soon as her mehram leaves, a man who is unrelated to her is then alone with her in a public area? What all can occur? That is what this means, and you'd be hard pressed to find a single scholar who disagrees.

that means that she doesn't have to maintain her awrah (wear hijab) in front of them. But if she is out in society then she should maintain her awrah and guard what is nessescary

You omitted the ayat before 31 that I provided. Allow me to put it once again:

An-Nur 24:30

قُل لِّلْمُؤْمِنِينَ يَغُضُّوا۟ مِنْ أَبْصَٰرِهِمْ وَيَحْفَظُوا۟ فُرُوجَهُمْۚ ذَٰلِكَ أَزْكَىٰ لَهُمْۗ إِنَّ ٱللَّهَ خَبِيرٌۢ بِمَا يَصْنَعُونَ

Tell the believing men to reduce [some] of their vision and guard their private parts. That is purer for them. Indeed, Allah is [fully] Aware of what they do.

So now we have the men must lower their gaze (i.e. not stare/gawk at the women), and that the women must protect their awrah with hijab. So let's go ahead and pair that with the hadith earlier.

A man and woman cannot:

Be alone together.

Be with one another without a mehram present whenever possible.

A man must LOWER HIS GAZE around a sister, meaning he probably shouldn't even be looking at her if he can so control himself. If he cannot he should really work on self discipline.

A brother must also protect his private parts around sisters (and further, in general he should).

A sister must protect her parts through covering appropriately with hijab, as well as taking the necessary precautions like having a mehram.

With all of this - how do you justify not agreeing with gender separation?