Merci! J'avais manqué une autre connexion: changeset/158796575

"But most roads with bike lanes in the montreal area are tagged with bicycle=designated"

Would you please provide a few examples? I have a couple that prove the contrary:
way/22910373
way/455264712

There's no ambiguity. The link you sent contains this language:
"object is *explicitly designated* for use by cyclists"

The whole way (the "object") is *not* designated for use by cyclists, only the two bike lanes on the side of the road.

That road is "designated" for bike use as much as it is designated for motor vehicle use.

Please check access=designated

This is a regular two-way street, with **two lanes for motor vehicles in each way,** which happens to have a bike lane on one site. Tagging it as a designated street for bikes is wrong.

Thanks for the heads up. I just fixed it: changeset/117896222

BTW, none of the nearby streets have those tags. :(