Measure shortest distance between all points in a layer and a polygon's border line

You can also use saga snap point to line (processing). That gives you the option on moving the point or producing a line. That line however will not be snapped because of float point errors but the distance will be good.

Finding the point distance to the boundary of a polygon for points that are inside can't be done directly as the proximity tool evaluates the distance from point to polygon as 0. To find the shortest distance of a point inside a polygon to its boundary degenerate the polygon to its bounding line, this link is different to the comment and has nice pictures.

After the polygon is reduced to its bounding line the distance can be calculated with v.distance and probably using NNJoin as you say but I can't attest to that having not used the NNJoin tool (yet).