I'm personally of the opinion that unless the path is actually signed to be a cyclepath, or if the path is too narrow for a cyclist to pass a pedestrian without needing to dismount first, then the path should be marked as a footway.
Per access rights, bicycle=yes would be appropriate too I think.
And in an ideal world, routing software could account for the width tag to discourage this footway if narrow, but I don't think there's any such software that does so alas.