Port the Geometry Snapper plugin to processing
Snap geometries algorithm allows snapping to other layer types, supports point/line layers
Snap to layer algorithm accepts a mode parameter. With a new option to prefer to snap to closest point on geometry. The old behaviour was to prefer to snap to nodes, even if a node was further from the input geometry than a segment. The new option allows you to snap geometries to the closest point, regardless of whether it's a node or segment.