You’re doing the right thing OP.
Much more important to your DS than the incident itself, is that’s he’s learning from you HOW this stuff should be handled.
As he watches you challenge the school administration - people he’s been taught, by you and probably most other people in his life, to trust and look up to - he will learn how to deal with racial discrimination and other forms of injustice, and how to deal with bullies. It’s crucial you don’t let it drop.
I’m a child of the 80s, London suburbs. I was called the same thing (not even Pakistani, but hey) by the ‘gang leader’ of a friendship group of four girls. They were just children, and obviously learned all this stuff at home, and everyone knew they didn’t truly grasp the weight of what they were saying, only that it was powerful and negative. My dad went quietly ballistic with the head teacher who did all the things your DS’s head is doing (so depressing this is still the case 30 years on): denied it happened, denied it was a big deal, made excuses for the girls, eventually extracted a pitiful apology etc. When my dad didn’t get the response he wanted, which was a commitment to ensuring they wouldn’t stand for such discrimination and that they would educate, he withdrew me from the school and explained why. It was essential to him that I understood I wasn’t running away from bullies, that these girls needed to be taught and they weren’t inherently bad aged 8, but that an environment where I was deemed less deserving of pastoral care for race-based problems than kids who were suffering other problems that required pastoral attention, was not the best thing for me (or indeed any child).
His dignity, sense of justice and fairness, his care for that group of girls, his soft and calm tone at all times (although I remember his eyes flashing with rage 30+ years on!), his determination to do his best for everyone (not just me as his child) - these things have stuck with me and set my moral compass. Such an important life lesson.
Come back here for support if you need it.