The features provide you a guarantee that you can hide
The rules say that you cannot hide when another creature can see you clearly, and that the DM gets to decide when you can (your clause 1. and 2.). This is not quite the same as saying that you can hide when the other creature cannot see you clearly. It might be be that you can, or it might be that you cannot, the DM gets to decide.
The DM decides when circumstances are appropriate for hiding. You can't hide from a creature that can see you clearly
Lightly obscured is described as follows
In a lightly obscured area, such as dim light, patchy fog, or moderate foliage, creatures have disadvantage on Wisdom (Perception) checks that rely on sight.
This does not outright say that creatures cannot see you clearly in a lightly obscured area, it only says they have disadvantage on sight based Perception checks. To be honest, to me that sounds as close to not being able to see clearly as one can get. What else would disadvantage on sight based perception represent, if not that you cannot see clearly?
But even if that is so, the DM still gets to decide if you can hide or not, because there is no rule that you always can hide when not seen clearly, there is only one that says you cannot, when seen clearly.
If you have either of these two features, you are not dependenddependent on your DM's decsiondecision any more because these say:
You can try to hide when you are lightly obscured from the creature from which you are hiding [Skulker]
You can attempt to hide even when you are only lightly obscured by foliage, heavy rain, falling snow, mist, and other natural phenomena. [Mask of the Wild]
In addition, Skulker provides some other benefits. The guarantee that you can hide "even when only lightly obscured (by natural phenomena)", also does not neccesarilynecessarily mean that you cannot hide if lightly obsucredobscured in general, as it refers to these special sources of obscurement.
I think the hiding and light/darkenessdarkness rules are a mess, and it is likely that the designers just forgot to update these features when they errataed the hiding rule from saying that that you cannot hide from a creature that can see you, full stop, to saying that you cannot hide from a creature that can see you clearly.
For example, Goblins have a bonus hide action, and for a goblin ambush in a forest to work and allow them to hide in bushes using this action, they would need to be able to hide while only lightly obscured -- but they have no special feature for that. Until we get a revision D&D with these glitches hopefully fixed, each DM must decide if they want to use these rules as written, or not.