I am still trying to improve the mapping of cycleways/routes around places I know.
It is not fully clear to me what attributes are used to decide if a way is represented with a double red line on cycle.travel
on OSM, there is the option do design a line as pedestrian or bicycle and pedestrian; there is also the field "allowed access" which should in principle be used if there is an explicit sign allowing bicycle access, and the tags that contains eventually bicycle: yes, if there is no explicit sign but it is still OK for bicycles.
In some places, the situation is somewhat in between, like it is not really stated that this is designated bike path, but on the other hand this is a road, forbidden to cars and motorcycle which is part of an official cycle route. So it could definitively be represented in double red line.
Knowing how tags are used in cycle.travel would help me chosing the right attributes.