Blender 2.93 now has LineArt Grease Pencil built in!
Edit: Blender 2.93 is now stable and officially released! But I think Beer/Malt renderer is still in development afaik.
To add toonlines, press:
- Shift+A > Grease Pencil > Pick a LineArt option. I use Scene LineArt.

This adds a Grease Pencil object. You can select it and go to modifiers to change line thickness and other settings.
Note that you have to look through camera view to see the outlines lined up properly.
If you want to orbit the camera around like the viewport:
- Press N-key to open up the side panel on the right
- Click the View tab.
- Checkmark Lock > Camera to View.

It's real-time on my slow old PC, but things start to slow down for me at higher vert counts. To get rid of lag, try this:

It works in any viewport (solid, material, eevee, etc.). EDIT: lines don't line up properly in other camera views on my PC when using simple "shader" and viewport render animation. I have to use actual render, which doesn't use this simple "shader". You can get a very simple toon "shader" in Material viewport (see pic).
(P.S. I can't get multi-colour toon shading to work like you did for some reason).
For a simple multi-colour shader, use these nodes with your material:

Here's a video:
https://www.youtube.com/watch?v=L791csCEJBg&t=608s
Another option is: BEER/MALT Renderer from blendernpr.org. STILL IN DEVELOPMENT. SO USE AT YOUR OWN RISK:
https://bnpr.gitbook.io/beer-malt-wiki/
https://github.com/bnpr/Malt