While I agree this looks to be marked as a bridleway on the OS map - the Gloucestershire definitive map shows this to be a footpath only (CWE86) https://maps.gloucestershire.gov.uk/MapThatPublic/Default.aspx

This doesn't seem like the correct edit. The underpass and the paths still exist but the underpass has been closed off now so cannot be used to pass under the road.

For the first one - because there is a gap on the South Gloucestershire definitive map data between LPU 48,49 and LPU 47. This can be seen on the overlays at https://osm.mathmos.net/prow/progress/south-gloucs/-/pucklechurch/ or when importing the footpath data as an overlay for JOSM.
For the second point - that makes some sense. I'll bear that in mind.

The exported data from south gloucs council. Mostly via https://osm.mathmos.net/prow/progress/south-gloucs/-/cold-ashton/ but also imported into QGIS. The council footpath prow_ref do not include the sub-section number. That's part of the key in the export data (visible in QGIS). I know the SGC online map has the sub-section (keyid) parts being shown.

Looks like I can move all the sections from the newer relation into the other so I'll do that.

After seeing so relation for this path I created one that already has more continuous coverage than the earlier one that I found later. My intention is to get the both merged. The original has a few unconnected segments. If I'd managed to find this earlier relation I'd have used it.