Where has the Vertex Colour node gone?

Shift+a->Input->Color Attribute. I believe you can also access it from Attribute node, but I’m not totally sure on that. 

Always always remember, that if it gets too frustrating the not finding things, you can use the Blender version used on the video.

Hey @eralp_orkun-cihan,
Blender changes regularly, the core skills of 3d do not.

While learning 3d as a beginner, it is far easier to learn by using the Blender version used in the course or tutorial. 
Not worrying about the UI and feature changes between Blender versions means students can concentrate on learning the 3d skills being taught, which are transferable across Blender versions and even other 3d software.

The more experienced Blender users will have less issues when following a course or tutorial with the latest version, because they will know about the differences and where a tool or setting has moved to.

It is impossible to release a new course on every topic in Blender with every version.
We recommend using the Blender version as in the course to learn the skills of 3d, learning Blender will naturally happen with time.
Ultimately, learning the 3d skills required for a project take priority over latest Blender version.