I’m glad to see that the final proposal doesn’t require explicit tagging for bicycle=yes in conjunction with cycleway:both=no, a double tagging requirement which would’ve made it less accessible for new editors, more error prone and in generally overly complex. I admit that I was concerned when I read that in the first draft. 
The current proposal aligns nicely with the sidewalk= mechanism (allowing for sidewalk=left/right/both and sidewalk[:left/right/both]=). However, that should also imply that cycleway=no is also allowed (instead of and/or as a shorthand of the longer cycleway:both=no) and should probably be documented and added to the example?
It was done prematurely, and addressed as such here, just not corrected yet.
It seems to me like the person who did the restructure understood the tag to be deprecated entirely, while the previous version of the page clearly indicated* that it was only deprecated in conjunction with highway=cycleway and not in conjunction with other highway='s, such as the in the proposal mentioned highway=residential. In other words - they were a bit over enthusiastic, it seems, in the clean-up of what’s deprecated and not.
*) Old wiki text I'm referring to
From this version:
cycleway=shared
In general, this indicates that cyclists share the road space with other traffic.
Note: This has also formerly been used on cycleways which were mapped as separate ways tagged as highway=cycleway before the segregated=* tag was formalized. Its use with highway=cycleway is now considered obsolete.
Emphasis mine.
Edit: Oh, I see now it was actually you who did that clean-up. 
Hi 
- maybe you could actually elaborate on it yourself then (either here or in the other topic) instead of me making assumptions. 