I was confused as the signs say 'National Cycle Network' but have 55 in a box with a blue background. Happy to change this back to regional if that better suits the designation.

Thanks for your help, I think perhaps the tag cycleway=shared_lane would be more appropriate then. With that tag the infrastructure is readable as it does add some benefit to wayfinding, despite that being minimal at best.
It seems a number of cycle routes (with a few notable exceptions) in Birmingham are currently marked on OSM as routes, but are made up of 1057s and/or bus lanes, with some other infrastructure e.g. at major junctions. I will review those I am familiar with.
Therefore, on this route the best way forward seems to me to be deleting the route and adding 'shared lane' tags to the streets.

The source was Birmingham City Council, but I did check using Google Street View. I realise now this is not best practice.
There are painted cycle symbols on the road which a cyclist can follow.