The problem with numbering I think is difficultly solvable is that a same stage relation can be part of several route relations. I.e. a stage part of ViaRhôna and EV17 should have two different numberings for the two different relations. Maybe it’s not an information that useful, as numbering can be retrieved by reusers by the ordering in the route relation.
@Florange_Grimoire if you have any insight on that matter?
For reference, Nadjita’s proposition: https://wiki.openstreetmap.org/wiki/User:Nadjita/Routes#Tag_stage=*