Thanks for your interest. These cycle markings were added when what was formerly a gyratory was returned to two-way in order to raise driver awareness cyclists might be present. They don't create a route, just like SLOW markings don't create a slow travel route! Also LB Southwark (the highway authority) does not consider this as a route in any of its transport or other documents.

When I get back from hols I will post something to talk-osm-gb as the question of what is a cycle route is often misunderstood in the UK in particular in London and is divergent from other countries. So your point is very much worth wider discussion.

Yes they should, sorry wasn't sure if changing the tag would do that or not. And didn't know how easily to change all the individual ways (at least for Phase 1 not 2A or 2B) to construction.

There should be an updated dataset following Royal Assent (minor changes such as longer tunnel in a few places). I can request this if someone else can upload it to OSM.