For now it would be best to focus this implementation on Sculpt Mode, since this will be the basis of the upcoming Paint Mode.

Issue

When using an image texture in a brush you can enable the option "Rake" so that the texture rotation is following the direction of the stroke.
This has a huge issue that it stamps the entire texture repeatedly which makes it impossible to create a smooth curved texture that accurately follows the stroke.

Proposal

Essentially we need to implement a way to split up the brush texture into many thin slices and apply them to the stroke incrementally.
This way it will have the visible effect of putting the texture on a paint roller and rolling it over a surface.
This would also make it possible to assign a very wide texture to a brush and paint it in a curved way on the surface.

Adjusting the texture size should help to redefine how stretched the used texture is:

Size = 1

Size = 0.25

Size = 2

Open Questions

It still needs to be discussed how this setting will be exposed and how it relates to the mapping, stroke and rake setting.