Cannot switch Framebuffers

I am trying to implement multi pass rendering using the OpenTK bindings for OpenGL. My approach is to render to a intermediate framebuffer and then using use that result to render the second pass. So far I have been following the official tutorial on framebuffers.
I have run into some issues while following the tutorial:

This is my code to render to the screen with one shader, which works fine:

GL.ClearColor(0.2f, 0.3f, 0.3f, 1.0f);
GL.Clear(ClearBufferMask.ColorBufferBit);

_texture.Use(TextureUnit.Texture0);
_shader1.Use();
GL.BindVertexArray(_vertexArrayObject);
GL.DrawElements(PrimitiveType.Triangles, _indices.Length, DrawElementsType.UnsignedInt, 0);

My approach to implement a second rendering pass following the tutorial:

// Pass 1
GL.BindFramebuffer(FramebufferTarget.Framebuffer, _framebuffer.Handle);
GL.ClearColor(0.2f, 0.3f, 0.3f, 1.0f);
GL.Clear(ClearBufferMask.ColorBufferBit);

_texture.Use(TextureUnit.Texture0);
_shader1.Use();
GL.BindVertexArray(_vertexArrayObject);
GL.DrawElements(PrimitiveType.Triangles, _indices.Length, DrawElementsType.UnsignedInt, 0);

// Pass 2
GL.BindFramebuffer(FramebufferTarget.Framebuffer, 0);
GL.ClearColor(0.2f, 0.3f, 0.3f, 1.0f);
GL.Clear(ClearBufferMask.ColorBufferBit);

_framebuffer.IntermediateTexture.Use(TextureUnit.Texture0);
_shader2.Use();
GL.BindVertexArray(_vertexArrayObject);
GL.DrawElements(PrimitiveType.Triangles, _indices.Length, DrawElementsType.UnsignedInt, 0);

The above code results in a blackscreen. Testing the everything individually yields the expected results. When I change the FramebufferTarget parameter of the firstGL.BindFramebuffer call to FramebufferTarget.ReadFramebuffer I get the output with ONLY the second shader applied. Anything else results again in a blackscreen.
Why does this happen, what is my mistake here? If anything, shouldn’t one expect the output in the above scenario be the combination of both shader passes? I am using shaders ‘NoRed’ and ‘NoGreen’, which when tested individually do what expected, so I think I am not misinterpreting the output.
I don’t often write community posts, and this might be a really stupid question, but even so I would really appreciate an answer.