C# an error when passing an unassigned out argument

I was wondering why I get an error in the following code? I am passing an unassigned integer x to foo using an out argument. I also assign a value to x before returning it to the calling method.

int x;
Foo(out x);
Console.ReadLine();
void Foo(out int y)
{
    Console.WriteLine(x); // x is 0
    y = 1; // Mutate y
    Console.WriteLine(x); // x is 1
}

This is strange because in the following code I can pass an unassigned string using similar principles and don't get back any errors.

string a;
Split("Stevie Ray Vaughn", out a, out _);
Console.WriteLine(a); 
void Split(string name, out string firstNames, out string lastName)
{
    int i = name.LastIndexOf(' ');
    firstNames = name.Substring(0, i);
    lastName = name.Substring(i + 1);
}

The Console.WriteLine calls from inside the Foo method can't compile unless x is a field, and not a local variable in the calling method.

If x is a field, then it automatically gets initialized with its default value, and since it's an int, the default value is 0. So code like this kind of makes sense. It will compile and run as you expected:

class C 
{
    int x;

    public void M() {      
        Foo(out x);
    }
    
    void Foo(out int y)
    {
        Console.WriteLine(x); // x is 0
        y = 1; // assing a value to y
        Console.WriteLine(x); // x is 1
    }
}

The output of this will indeed be 0 and 1 as you can see in this SharpLab demo.

However, if x was a local variable in the calling method, you'll get compilation errors on the two lines in Foo that are attempting to use it:

> error CS0103: The name 'x' does not exist in the current context

Here's the SharpLab demo of that.

Now suppose you'll change the x in these lines to y:

class C 
{
    public void M() {      
        int x;
        Foo(out x);
    }
    
    void Foo(out int y)
    {
        Console.WriteLine(y);
        y = 1; 
        Console.WriteLine(y); 
    }
}

Here's what will happen: You'll get an error on the first line calling Console.WriteLine(y);

> error CS0269: Use of unassigned out parameter 'y'

Demo here

But if you remove the first call to Console.WriteLine(y);, everything will work perfectly - as shown in this demo.

So, to conclude - the problem is not where you thought it was.
It's absolutely fine to pass down unassigned local variables as out parameters to methods, as long as you're not using them before their first assigned a value.