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Edit(2):

//.... just like above
out vec2 TexCoords;

void main()
{
    //.... just like above
    float texX = position.x / texSize.x + 0.5f;
    float texY = position.y / texSize.y + 0.5f;
    TexCoords = vec2(texX, texY);
}

Edit(2)(3):

//.... just like above
out vec2 TexCoords;

void main()
{
    //.... just like above
    float texX = position.x / texSize.x + 0.5f;
    float texY = position.y / texSize.y + 0.5f; 
    // if you need to flip image, use texY = 1.0 - texY; here
    TexCoords = vec2(texX, texY);
}

Start Edit:

Start Edit(1):

Edit(2):

The texCoord part, I did it and share here :)

//.... just like above
out vec2 TexCoords;

void main()
{
    //.... just like above
    float texX = position.x / texSize.x + 0.5f;
    float texY = position.y / texSize.y + 0.5f;
    TexCoords = vec2(texX, texY);
}

I sloved this by changing the GUI system to pass real position instead of normailzed position, just an example conecpt here:

float vertexPosition[] = 
{
  //  x         y
  -1.0f/2.0f,  1.0f/2.0f, // top left
  -1.0f/2.0f, -1.0f/2.0f, // bottom left
   1.0f/2.0f,  1.0f/2.0f, // top right
   1.0f/2.0f, -1.0f/2.0f, // bottom right
}

And for each vertexPosition, I multiply it by texture's Width and Height.

for (int i = 0; i < length; i++)
{
    if (i % 2 == 0)
        vertexPosition[i] *= (float)width;
    else
        vertexPosition[i] *= (float)height;
}

Then we got the real position, and you should use glBufferData to update your vbo (note: you should bind the vao properly before), and in the shader do the normailize in the final output position, like this:

#version 330 core
in vec2 position;
uniform mat4 transformation;
uniform vec2 screenSize;
//out vec2 TexCoords;

void main()
{
    vec4 testPos = transformation * vec4(position.x, position.y, 0.0f, 1.0f);
    gl_Position = vec4(testPos.x / (screenSize.x / 2.0f), testPos.y / (screenSize.y / 2.0f), 0.0f, 1.0f);
}

You maybe have a final question, how could get the TexCoord in shader ? there is two option to get it. One option, pass a Texture Coord that you defined as a Vertex Attribtue in every loop, or if it is constant you should pass it out of loop. The other option is calculate in your shader.

In conclusion, the step of doing this is:

1. Pass the real position instead of normalized position.
2. Do your transformation in shader as usual.
3. Normalized your final position before you give it to gl_Position.

I sloved this by changing the GUI system to pass real position instead of normailzed position, just an example conecpt here:

float vertexPosition[] = 
{
  //  x         y
  -1.0f/2.0f,  1.0f/2.0f, // top left
  -1.0f/2.0f, -1.0f/2.0f, // bottom left
   1.0f/2.0f,  1.0f/2.0f, // top right
   1.0f/2.0f, -1.0f/2.0f, // bottom right
}

And for each vertexPosition, I multiply it by texture's Width and Height.

for (int i = 0; i < length; i++)
{
    if (i % 2 == 0)
        vertexPosition[i] *= (float)width;
    else
        vertexPosition[i] *= (float)height;
}

Then we got the real position, and you should use glBufferData to update your vbo (note: you should bind the vao properly before), and in the shader do the normailize in the final output position, like this:

Start Edit:

#version 330 core
// All positions should be half around the origin in ndc.
in vec2 position;
uniform vec2 translate;
uniform mat4 scale;
uniform mat4 rotate;
uniform vec2 screenSize;
 
out vec2 TexCoords;

void main()
{
    vec4 realPosition = rotate * scale * vec4(position.x, position.y, 0.0f, 1.0f);
    float normX = realPosition.x / (screenSize.x / 2.0f) + translate.x / screenSize.x;
    float normY = realPosition.y / (screenSize.y / 2.0f) + translate.y /screenSize.y;
    gl_Position = vec4(normX, normY, 0.0f, 1.0f);
}

You need to pass translate seperately, because we use real postion, otherwise, you might need to compress translation outside and make a matrix.

End Edit

You maybe have a final question, how could get the TexCoord in shader ? there is two option to get it. One option, pass a Texture Coord that you defined as a Vertex Attribtue in every loop, or if it is constant you should pass it out of loop. The other option is calculate in your shader.

In conclusion, the step of doing this is:

1. Pass the real position instead of normalized position.
2. Do your transformation in shader as usual.
3. Normalized your final position before you give it to gl_Position.