Bit packing issues!

Hello, I need help in understanding and solving a problem where my CPU is correctly (and I have verified) packing vertex position data into a 32 bit integer, but my GPU is unable to properly extract the bits therefore unable to draw triangles.

CPU side

// This formats the vertex array object so that the gpu understands how to traverse the vertex buffer
void ChunkMesh::Format() {
    glEnableVertexArrayAttrib(VertexArray(), 0);
    glVertexArrayVertexBuffer(VertexArray(), 0, VertexBuffer(), 0, sizeof(ChunkVertex));
    glVertexArrayAttribFormat(VertexArray(), 0, 1, GL_UNSIGNED_INT, GL_FALSE, 0);
    glVertexArrayAttribBinding(VertexArray(), 0, 0);
}

ChunkVertex::ChunkVertex(const std::uint8_t x, const std::uint8_t y, const std::uint8_t z, const std::uint8_t textureIndex, const std::uint8_t corner, const std::uint8_t face) {
    uint8_t* ptr = (uint8_t*)&packed;
    ptr[0] = x | (z << 4);
    ptr[1] = y;
}

Vertex Shader

#version 430 core

in uint packedData;

// Yes, this is set.
uniform mat4 projection;
uniform mat4 view;

// Yes, this is also set.
uniform vec2 chunkPosition;

// Do not worry about this
const float brightness[] = float[6](
  // Up, Down, Left, Right, Front, Back
  1.0,   0.2,  0.5,  0.2,   0.75,  0.3
);

void main() {
  // The problem:
  uint x = packedData & 0xFu;
  uint z = (packedData & 0xF0u) >> 4;
  uint y = (packedData & 0xFF00u) >> 8;
  vec3 position = vec3(float(x), float(y), float(z));
  gl_Position = projection * view * vec4(position + vec3(chunkPosition.x, 0.0, chunkPosition.y), 1.0);
}

The fragment shader simply outputs red.