In case anyone is interested, here's my take on the Hide action. The intent behind it was to clarify how hiding works, formalize the use of the Hide and Search (which is an action that I think is largely ignored) actions, and reduce rolling by making the active character roll against the passive score of their opponent.
In order to take the Hide action, a creature must either be in an area that is heavily obscured, or have some physical obstacle that can be used to block line of sight. Exceptions to this include Wood Elves who can attempt to hide in areas that are lightly obscured, or Halflings who can attempt to hide behind creatures of Medium size or larger.
When a creature takes the Hide action (the hider), and there are others in the area that could conceivably see the hider (the lookers), then the hider makes a Stealth check contested by the passive Perception scores of any lookers. Lookers take a -5 penalty to their passive Perception score if they are in an area that is lightly obscured, or would otherwise have disadvantage on a Perception check. The hider is hidden from any lookers he beats, but is noticed by any lookers he doesn’t. The hider automatically succeeds against any lookers who are in an area that is heavily obscured.
On a looker’s turn, if they cannot see the hider then they can use the Search action to attempt to find the hider. The looker then makes a Perception check opposed by the hider’s passive Stealth score. The hider has a -5 penalty to their passive Stealth score if they would have disadvantage on their Stealth check. If the looker has allies with whom they can communicate who can see the hider, then the looker has advantage on this roll. A looker who is in an area that is lightly obscured has disadvantage on this roll, and they automatically fail if they are in an area that is heavily obscured. If the looker’s Perception roll beats the hider’s passive Stealth score, then they can see the hider and they are no longer hidden to that looker.