I think you're confusing a few things, so let me explain them before answering your questions.
Blender comes with pre-built setups (App Templates) focused on specific types of work. They can be accessed from the splash screen shown below. It seems that you're using the 2D Animation App Template.
The 2D Animation App Template includes four pre-built Workspaces which are the tabs you see at the top. Each Workspace is just an arrangement of Editors. The Workspace tabs are marked red in the screenshot below, while the Editors are indicated by blue borders.
You can customize any of these. You can customize an App Template by adding other pre-built Workspaces to it by clicking the + tab. You can also customize a Workspace by switching the Editor types it includes. The + tab is marked red, and the Editor type button is marked blue in the screenshot below. Clicking the Editor button for any of the Editors allows you to select a different Editor to switch to.
With the UI concepts out of the way, I want you to know that the 2D Animation App Template is intended for 2D animation by drawing with Grease Pencil. I don't think that's what you're doing, since your puppet is a mesh. I suggest to start with the General App Template. Just because you're working in 3D doesn't mean you have to output a 3D animation. In fact, the 2D Animation App Template is still in 3D, but it is set up in such a way that the 3rd dimension is ignored.
The answer you received on the question you linked to is not using Geometry Nodes. It is using Shader Nodes. Please note that Nodes are used in a number of Editors in Blender.
Are geometry nodes and the nodes editor reserved for 3D animation? If not, how can I access them in 2D animation?
No, they are not. You can access them by clicking the Editor type icon. You can also add the Geometry Nodes Workspace as shown below. I don't think that's what you need to do, though. I explained above.
Are nodes specific to 3D
No. There are different node systems in Blender (Shader nodes, Geometry nodes, and Texture nodes). They can be used for 3D or 2D. I suggest to stick with the Shader nodes for now, as the answer your received is using it.
If you want to continue following the answer you received. Switch one of the Editors to the Shader Editor or add the Shading Workspace. The Value node can be found in the add menu as shown.
If something is not clear, please feel free to comment below.