Tags on a way apply to the way object itself and not any other sidepaths that would somehow have to be inferred by data consumers. I.e. this:
Substantial discussion is already here and this question only came up because of SC, so I think it’s appropriate.
Anyway, speaking as someone who’s had to fix several cycleways recently because someone using StreetComplete removed the oneway:bicycle=no tag, please make doubly sure that whatever SC ends up doing doesn’t lead to more (unintentional) breakage.