At least according to https://wiki.openstreetmap.org/wiki/Tag:highway%3Dcycleway, you can use either highway=path or highway=cycleway (along with the other tags you mentioned) for this sort of situation  without any sort of difference, so IMO it doesn't make much of a difference either way. I do  however think that it should be one way considering you can go from the sidewalk to the bike lane portion without any large effort.