Ah, ok. These forums are for the Microsoft Maps (Bing and Azure Maps) platforms and unrelated to the Bing Maps consumer site, thus the confusion. I know that document your referenced. The collection functionality that existed when that doc was written isn't the same thing that is on bing.com today and I think it mainly still documented for legacy purposes as the old collection data is still available.
That said, it looks like the new collection functionality does reuse some of the old stuff, just the cid is not exposed through the user interface (you are meant to use the share button to get the sharable link). The way I managed to get the cid when testing is by going to the tab that shows the list of all my collections, then right clicked on the one I wanted and pressed "Inspect", then looked for the "data-entityid value" in the HTML source code as shown below: