The outline around the outside of the view is actually a 2-part effect. The farthest edges of the screen are converted to a paper-like texture. The area just inside this has been oversaturated to help give more visual interest to the edges of the screen.
This is primarily achieved by using a special screen-aligned texture. The texture uses the R, G, and B channels to hold masks. Below is the texture, as well as each channel separated.
By masking out the edges of the screen with the Green channel and then overlaying a noisy paper-like texture and color, the effect is given that the scene has been painted onto a piece of paper.
On top of all of this, the paper texture is multiplied across the entire view, giving a paper grain effect to the whole scene.
The heart of this system lies within the Paper Mask comment area. This network uses the texture shown above, but makes use of a ScreenAlignedUVs Material Function. This takes the texture coordinates and applies them to the screen extents, effectively stretching the texture across the screen. When used as part of a Post Process Material, the result is a texture that perfectly fills the view.