Hi,
first of all, the term bike_network in GH does not care about real infrastructure such as cycleways but it only takes (bicycles-)routes into account.
The definition of a bicycle route in OSM can be found here:
https://wiki.openstreetmap.org/wiki/Tag:route%3Dbicycle
To get a better unterstanding, here is a overpass-query for your area of interest:
Also I made a query with “real” cycleways in OSM for your area of interest:
In blue you see the separate cycleway infrastucture, that is also considered as road_class == CYCLEWAY in GH. Then in green there is cycleway infrastucture that is tagged not separatly but as an attribute of a road/highway. The GH-roadclass here is not cycleway but rather the corresponding highway-type in OSM, which I tried to describe also in here:
To achive what you want (routing on cycleway infrastucture?) you rather need customize the priority weights for road_class, however, in my understanding the not-separated cycleways (see green-colered ways in the query above) can not be taken into account in GH, so far. (?)
I simplified your example:
You can play around with the weights of
road_class == CYCLEWAY
bike_network == MISSING
to get a better unterstanding.
Disclaimer: I am quite new to GH, however know OSM pretty well. I am happy to be corrected.