Drag the link of the quest to an individual PC portrait to share with the owning player.
That is correct, this is by design on the player side. The idea being that only a few things would ever be shared with the players at any one time. The devs have answered the reasoning behind this recently, but can't find it at the moment.
EDIT: If the individual player want to do some form of organisation, they can put a bunch of links in a "note" that they own. But, of course, if the GM stops sharing a record the link will no longer be valid.

