How do I simulate C#'s {get; set;} in C++?

TL;DR: Don't

What you have isn't a getter, it's just a normal data member that's calculated once when the object is initialized.

In general, C++ doesn't support C#-style properties. The usual C++-style solution is to just use a pair of member functions (and maybe a data member, if you need to save the value separately), i.e.

struct Vector2 {
    // ...

    float length() const { return sqrt(x * x + y * y); }
    void length(float l) {
        float angle = angle();
        float new_x = l * cos(angle);
        float new_y = l * sin(angle);
        x = new_x;
        y = new_y;
    }

    // ...
};

You can get something close to a C#-style property, but you'll always run into edge-cases where they don't work perfectly. For example, here's something that will work in many cases:

template <typename T>
class Property
{
private:
    std::function<T()> getter_;
    std::function<void(const T&)> setter_;

public:
    Property(std::function<T()> getter, std::function<void(const T&)> setter)
        : getter_{getter},
          setter_{setter}
    {}

    operator T()
    {
        return getter_();
    }

    const T& operator=(const T& val)
    {
        setter_(val);
        return val;
    }
};

struct Vector2
{
    float x;
    float y;
    Property<float> length{
        [this]() { return sqrt(x * x + y * y); },
        [this](float l) {
            float new_x = l * cos(angle);
            float new_y = l * sin(angle);
            x = new_x;
            y = new_y;
        }
    }

    Property<float> angle{
        [this]() { return atan2(y, x); },
        [this](float a) {
            float l = length;
            x = cos(a) * l;
            y = sin(a) * l;
        }
    }

    // ...
};

int main() {
    Vector2 v;
    v.x = 1;
    v.y = 1;

    v.angle = std::numbers::pi / 2;
    std::cout << "(" << v.x << ", " << v.y << ")\n";
}

But this still falls apart in the edge cases, especially when you mix it with templates and/or auto type-deduction. For instance:

Vector2 v;
v.x = 1;
v.y = 1;

auto old_angle = v.angle;
v.angle = std::numbers::pi / 2;

// oops, this prints pi/2, not pi/4 like you probably expected
// because old_angle isn't a float, it's a Property<float> that
// references v
std::cout << old_angle << '\n';

Note also that there's a bug here. Consider this:

int main() {
    Vector2 v1;
    v1.x = 1;
    v1.y = 1;

    Vector2 v2 = v1;
    v2.angle = std::numbers::pi / 2;

    // Oops, assigning to v2.angle modified v1
    std::cout << "(" << v1.x << ", " << v1.y << ")\n";
}

You could work around these issues by making Property non-copyable, but then you force any class that uses it to implement a custom copy-constructor. Also, while that would make the auto case "safe", it does so by turning it into a compile error. Still not ideal.

I agree with Miles. This is not the greatest idea, because it's unnatural for C++ developers, and you should write code that is first and foremost easy to read.

However, as an engineering challenge, here's a possible implementation:

#include <math.h>
#include <iostream>

template <typename T>
class Member
{
public:
    operator T() const { return _value; }
    void operator =(const T& value) const { _value = value; }                                                                                                                                                             void operator =(T&& value) { _value = std::move(value); }
                                                                                                                                                                                                                      private:
    T _value;
};

class Angle
{
public:
    Angle(const Member<float>& x, const Member<float>& y) :
        _x(x), _y(y) {}

    operator float() const { return atan2(_y, _x); }

private:
    const Member<float>& _x, _y;
};

class Obj
{
public:
    Member<float> x, y;
    Angle angle;

    Obj() : angle(this->x, this->y) {}
};

int main()
{
    Obj o;
    o.x = 3;
    o.y = 5;
    std::cout << o.x << ", " << o.y << " -> " << o.angle << std::endl;
}

While other solutions also seem to be possible, this one seems to be the most elegant :P

using namespace std;

struct Vector2 {
    float x;
    float y;
    float init_length = [&]()-> float {return sqrt(x * x + y * y); }();
    float init_angle = [&]()-> float {return atan2(y, x); }();

    __declspec(property(get = GetAngle, put = SetAngle)) float angle;
    __declspec(property(get = GetLength, put = SetLength)) float length;


    Vector2() : x(0), y(0) {}
    Vector2(float a, float b) : x(a), y(b) {}
    ~Vector2() {}
    Vector2(Vector2& other) : x(other.x), y(other.y) {}
    Vector2(Vector2&& other) = delete;
    void operator =(Vector2&& other) = delete;

    void Display() {
        printf("%f\n%f\n%f\n%f\n\n", x, y, length, angle);
    }

    float GetLength() {
        return sqrt(x * x + y * y);
    }

    float GetAngle() {
        return atan2(y, x);
    }

    void SetLength(float l) {
        float a = GetAngle();
        x = cos(a) * l;
        y = sin(a) * l;
    }

    void SetAngle(float a) {
        float l = GetLength();
        x = cos(a) * l;
        y = sin(a) * l;
    }
};

int main()
{
    Vector2 vec = Vector2(10, 17);
    vec.Display();
    vec.length = 5;
    vec.Display();
}