It is better changed to gbfs:*= to follow gtfs:*= . That was being voted on. Proposal:GTFS Tagging Standard - OpenStreetMap Wiki
ref:*= suffix should be used for different databases and systems, not exactly different formats. All companies will use the GBFS format.
ref:gbfs= is currently an artificial identifier made up for OSM, composed from system_id and station_id . If needed, the ref= of the =bicycle_rental itself should be based on the station_id only.
For data tracking purposes, gbfs:*= should then be used. It can be separated into gbfs:system_id= and gbfs:station_id= . This is simpler to use. I can search for all Docomo stations with gbfs:system_id=docomo-cycle directly based on GBFS specification. No need for regex, which is further slower and less efficient.
The extensibility of gbfs:*= will allow other info to be added in the future easily and authoritatively. Eg gbfs:region_id= for Docomo. This confirms the network= .