I might be misunderstanding the question. When cycle infrastructure is mapped onto a main roadway, the flow of bike traffic will be inline with driving on the right. So, a possible situation is to have a single lane for vehicular traffic and added bike lanes on both sides, that are both one way. But the left one is counter flow.
Having cycling paths on both sides of a road that are not oneway does happen. But then these cycling paths have separation and are mapped separately as highway=cycleway
.
Here some examples:
(Cycleways mapped seperate)
https://www.openstreetmap.org/way/1055102631
oneway=yes
+cycleway=lane
+oneway:bicycle=no
https://www.openstreetmap.org/way/6842020
oneway=yes
+cycleway=lane
https://www.openstreetmap.org/way/6501639