Yaw rotation not translating to Quaternion

Question

I'm trying to implement the gimbal lock fix described in this question, but I end up getting weird behavior where when I rotate on the X axis (or try to at least) it rotates on both the X and Y axis at the same time, but when i try and rotate on the Y axis nothing happens at all.

I'm keeping total orientation in a quaternion and (trying to) update it with a rotation matrix constructed by forward, right, and up vectors. I'm deriving these vectors like so:

// From https://learnopengl.com/Getting-started/Camera

_forward.X = (float) (MathHelper.Cos(MathHelper.DegreesToRadians(_rotation.Y)) *
                      MathHelper.Cos(MathHelper.DegreesToRadians(_rotation.X)));

_forward.Y = (float)  MathHelper.Sin(MathHelper.DegreesToRadians(_rotation.X));

_forward.Z = (float) (MathHelper.Sin(MathHelper.DegreesToRadians(_rotation.Y)) *
                      MathHelper.Cos(MathHelper.DegreesToRadians(_rotation.X)));

_forward.Normalize();
_right = Vector3.Cross(_forward, _worldUp).Normalized();
_up    = Vector3.Cross(_right, _forward)

and updating the _rotation values like this:

public void RotateX(float rotation) {
    _rotation.X += rotation * _sens;
}

public void RotateY(float rotation) {
    _rotation.Y += rotation * _sens;
}

To get the rotation matrix I'm just putting the 3 vectors into a Matrix3 object:

var r1 = new Vector3(_right.X, _up.X, _forward.X);
var r2 = new Vector3(_right.Y, _up.Y, _forward.Y);
var r3 = new Vector3(_right.Z, _up.Z, _forward.Z);

var mat = new Matrix3(r1, r2, r3);

if (mat != _check) {
    _orientation = Quaternion.FromMatrix(mat) * _orientation;
}
            
_orientation.Normalize();

and then I update the orientation quaternion.

The _check property is just a matrix that represents what should be created if there is no change in rotation so _orientation isn't changed when it doesn't have to be.

This is a gif of what happens when I just use the RotateX function, so it just rotates on some weird axis. Any clue what I'm doing wrong? Am I initializing the rotation matrix wrong or is it something else entirely?

[edit]

Camera pitch now works without affecting Yaw and Roll:

public void Update() {
        _forward.X = (float) (MathHelper.Cos(MathHelper.DegreesToRadians(_rotation.Y)) *
                              MathHelper.Cos(MathHelper.DegreesToRadians(_rotation.X)));

        _forward.Y = (float) MathHelper.Sin(MathHelper.DegreesToRadians(_rotation.X));

        _forward.Z = (float) (MathHelper.Sin(MathHelper.DegreesToRadians(_rotation.Y)) *
                              MathHelper.Cos(MathHelper.DegreesToRadians(_rotation.X)));

        // _forward.Normalize();
        _right = Vector3.Cross(_forward.Normalized(), _worldUp);
        _up    = Vector3.Cross(_right.Normalized(), _forward.Normalized());
            
        Console.Out.WriteLine("forward: {0}", _forward);
        Console.Out.WriteLine("right: {0}", _right);
        Console.Out.WriteLine("up: {0}", _up);
            
        var r1 = new Vector3(_right.X, _up.X * _worldUp.X, _forward.X);
        var r2 = new Vector3(_right.Y, _up.Y * _worldUp.Y, _forward.Y);
        var r3 = new Vector3(_right.Z, _up.Z * _worldUp.Z, _forward.Z);

        var mat = new Matrix3(r1, r2, r3);

        if (mat != _check) { // Change in orientation.
            _orientation = Quaternion.FromMatrix(mat) * _orientation;
            Console.Out.WriteLine(_orientation.ToEulerAngles());
        }
            
        _orientation.Normalize();
            
        Console.Out.WriteLine("Position: {0}", _position);

        _rotation = Vector3.Zero;
}

But no rotation occurs when trying to rotate about Y axis.

Answer 1

Thanks to DMGregory for correcting my quaternion understanding. All is working fine now. I just make a quaternion for pitch and yaw then multiply them with my existing oreientation quaternion like so:

// Values in _rotation are already converted to Radians.
var pitchQuat = new Quaternion((float) MathHelper.Sin(_rotation.X / 2f), 0f, 0f, 
                               (float) MathHelper.Cos(_rotation.X / 2f));
                
var yawQuat = new Quaternion(0f, (float) MathHelper.Sin(_rotation.Y / 2f), 0f, 
                                 (float) MathHelper.Cos(_rotation.Y / 2f));


_orientation = pitchQuat * _orientation * yawQuat;

This replaces the whole Matrix thing I was going with and actually makes the camera work like I wanted. Thanks again to DMGregory for just being cool.

Result(idk why the colors are freaking out it wasn't actually doing that it's just recording artifact i guess):