Example of construction highway (for next year at least) is https://www.openstreetmap.org/way/224483432. Which is currently rendered as https://tiles.phyks.me/#18/48.81797/2.31829 (small line).

Do you have an example with cycleways?

Alright I didn't saw them.
You have cycleway example on the famous Champs Élysée ;)
https://tiles.phyks.me/#18/48.86994/2.30738

So the ticket would changed to : better visualization, I can't barely identify them (which type of higway ?), I like the default OSM render like https://www.openstreetmap.org/#map=19/48.86968/2.30849

What's the status of this one? Do we have an updated example at hand?

Current status is that construction roads are not rendered
Cycleway example here https://www.cyclosm.org/#map=19/48.84389/2.37202/openstreetmap

Got an idea on this, we could transform highway=construction + construction=? into highway=? + construction=true in project.mml.

Then, the highway under construction would get the exact same render as the final one. Then, we need to distinguish the construction status of the way.

What about using transparency and dimming it out, just as we do for private POIs?

Dash line ? Transparency and dash line ?