"Bookmark" / "Read Later" Link that Saves a Page to a CB Tab

I'd like to have a function on my site, where a user can browse to any page on the site, and (maybe using a module or something in the template itself) can click that link (e.g. Bookmark or Read Later), that will save that URL onto a CB tab for that user to review later.

A sort of internal bookmarking system that applies only to the site and save those links to a CB profile for that user to review later.

Would be nice if they can leave notes on those pages too but that would be a bonus.

Anything out there, or anything I can do custom?

Maybe a custom code that grabs the current URL and writes it on a CB Tab Blog wall or similar along with notes?

We've nothing of the sort. You'd need to create a custom CB plugin to handle that. Tab URLs are &tab=TAB_TITLE_OR_TAB_ID for example. There's no API to grab the currently viewed tab URL, you have to construct that manually by appending &tab=TAB_TITLE_OR_TAB_ID to the URL.