Stateless Lambda and Private members

In certain cases when programming with libraries written in C involving callbacks, I like to use Lambda expressions; however, if I need to alter the state of a class member variable I can't juts pass this into a stateless(function pointer) lambda. But I can assign this to a data in a context structure. What I find strange is being able to access that member variable even if it's private in the class. Here's an example code I wrote to demonstrate.

#include <iostream>
using std::cout;
typedef struct extradatatype{
    void* data;
}extradata;
extradata e = {0};
typedef void(*callback)(extradata* e);
void cb(callback c){
    c(&e);
}

class Test{
private:
    int x;
public:
    Test(int x){
        this->x = x;
    }
    void setcb(){
        cb([](extradata* e){
            Test* self = reinterpret_cast<Test*>(e->data);
            self->x = 20;
        });
    }

    int getx(){
        return x;
    }
};

int main(){
    Test t(10);
    e.data = &t;
    t.setcb();
    cout << t.getx();

    return 0;
}

In the Lambda expression Test* self is assigned to e->data but I can access self->x as if it were a public member instead of private. So what I'm confused about is, is the lambda expression expression being executed within the stack/context of the setcb function or is it being executed elsewhere as its own function but C++ is doing some weird trick to allow private members to be accessed. Because I assume a stateless lambda is really no different than a non member static function which has no access to private members of a class.