Hello!

It is a bit more complicated than that. If we start looking at the law, then by definition of ID "designated" tag tooltip, any crossing is designated for cycling, literally any. The definition in ID for the tag is: "Access allowed according to local signs or specific local law." While tag yes means: "Access allowed by law; a right of way."

Since I am working with ID as the best tool I can use right now, I have been mapping crossings mostly with designated since ID tooltip gave such hint.

The WIKI says on the other hand for designated: "A preferred or designated route for the class of traffic specified by the tag key, such as foot=designated, in general this means that there is a (explicit) sign saying something like "pedestrians allowed", or a pedestrian icon."
While for the yes tag: "The public has an official, legally-enshrined right of access; i.e., it's a right of way."

Kind of complements the ID tooltips that are shown on access tags.

Now, if we start looking at local law, then literally its falling apart on any distinction of the access because anyone can cycle anywhere of any age despite various limits. Its the exceptions that allow any cycling on any path.
Hence why I have been tagging crossings with designated tag for cyclers. Its WIKI explanation is literally as wide as out local law regarding of cycling.

Same thing with footpaths, sidewalks etc unless there is specific sign that disallows usage of a path fir cyclers. The best example of this is the vehicle path in front of Kristiine keskus toward city center. There is explicit sign that disallows cycling on the vehicle path and cyclers must use the sidewalk.

Exact same problem is with pedestrians on cycling path. Our local law explicitly says that pedestrians are allowed on cycling road if there is low traffic on it. But how low or how high, is left to decide for the pedestrian and hence you can simply add once again "designated" tag for the cycling road for the pedestrian access.

So what I think about it? Well "it depends" is the answer here because of our law... Designated access tag had just so wide meaning that its basically safe bet to use if you dont know the area, dont have any street level imagery or any other kind of info that could set better tag for the path, area, crossing etc.

But we could come up with some simple rules anyway since slaping "designated" everywhere is a bit tedious in the end and does not give great feedback on what is actually at the site.