I've seen pictures like these online; how can I do this myself? I do see a color option under Viewport Display, but it seems like that would color an entire object rather than specific regions. I admit I haven't tried, though.
I think this can be achieved in solid mode by using "Vertex Color"
This video is a pretty good resource for learning more about it: https://www.youtube.com/watch?v=8mNk6r_bwxI
I was able to achieve the effect without affecting the rendered mode by doing the following:
Add a cube, switch to "Edit" mode and subdivide the cube.
Select a few of those faces.
Open the "Object Data Properties" panel and add a new "Vertex Color" a. It will say "Col" or "Col.001"
Switch your "Viewport Shading" "color" to "Vertex"
Switch to "Vertex Paint" mode and select the "Paint Mask" tool
Click on the selected faces and paint them compeletely
a. If you want to paint-bucket/fill them, Shift + k
Repeat with different colors for other faces
Switch back to object mode and observe the colored faces.
Switch to rendered mode and observe that the vertex colors aren't the actual rendered material.
a. You can actually use them as the rendered material - node setup for this is in that video.