Caveat: I don't think this is incredibly clear from the wording of the spell, so my answer will be subject to some semantic parsing.
No, that errata does not impact the effect of the Darkness spell.
The fact that "darkness" as opposed to "the effects of the Darkness spell" is listed as an example of a heavily-obscured area and that the spell description doesn't describe it as creating "a heavily obscured area" means that errata is kind of a red herring in this case.
The spell description says that a creature with darkvision can't see through it (which requires the logical leap that creatures without darkvision also can't see through it :) ), which means someone in the area of effect can't see out, since that would require seeing through some portion of the darkness.
A more grody scientific explanation would say that since "nonmagical light can't illuminate it," you can't see something unless light bounces off that thing and hits your eyes, and light that does do that would potentially be illuminating something in the darkness, so...no on that front as well (though if your game gets to the point of debating the nature of light itself, you might want to call it a day already).
I realized my comments were better suited as their own answer.
You are absolutely correct that a hooded lantern would be visible in the dark from any distance. Assuming you had direct line of sight on the lantern.
So if you are in an open empty field, or a very large open cavern, then you are right...there's no point to a hooded lantern.
However, you can only see light if you have line of sight on it. And, when seeing 'light' there are two things you may be seeing. You may either be seeing the source of the light (the lantern) or you may be seeing the area illuminated by the light.
So, where this becomes useful is in areas that do not have clear, long-distance visibility. Such as in a building, or a cave, or a forest, or city streets, or literally anywhere that is not an open field.
The way this works is this: If you have a hooded lantern and you have the hood up, you are casting a Sphere 60' aura of light around you. In an area with corners, doors, or any other obstruction that blocks line of sight, this means any creature that can see any part of that 60' radius aura of light...can see your light.
However, if you hood the lantern, that drops it to throwing off a radius 5' aura of light. Bearing in mind that spheres include their origin as part of the radius...this means that only the single square that the lantern is sitting in is illuminated, with a bit of bleed-over into the neighboring squares. This means that unless a creature gets line of sight on the squares immediately around the one the lantern is in, they cannot see the light.
There are several practical uses for this. While dungeoneering, the party can dim the lanterns to sneak up to a corner. If each party member carries a lantern, they can each see where the other is, and see the ground under their feet so they don't trip or anything...but no one around that corner can see them coming, because none of the light created by the lantern reaches around the corner to become visible. Then the elf sticks their head around the corner, using their Darkvision to see what's there...all without ever showing any light to the creatures around that corner.
On the other hand, if you wanted to try the same trick with a non-hooded lantern, the party members that can't see in the dark would have to stay 60' away from the corner, so that the light created by their lanterns didn't go past it and reveal their presence.
So, in summary...
Yes, a light is visible from a tremendous distance, IF you have line of sight on the light source, or anything the light source is illuminating. In an open field, this means dimming your light doesn't help much. But in an area with obstructions, dimming your lantern means you reduce the aura that is visible in the dark from a 60' sphere, to a 5' sphere. And given that this aura can shine past corners, under doors, through windows, and so on....reducing your light aura is very useful in areas with obstructed vision.
Best Answer
The fog cloud spell says (emphasis mine):
Unlike nonmagical darkness, other heavily obscured areas created by spells such as fog cloud do generally prevent creatures from being able to see through them (unless there is some feature, spell, magic item, etc. that allows them to do otherwise - such as the warlock's Devil's Sight eldritch invocation when it comes to the darkness spell).
The distinction is that nonmagical darkness doesn't involve stuff blocking your vision, just the absence of light in that area. If there's a light shining down at point A and another at point B, and there's a bit of mundane darkness in between (but nothing else obstructing your view), then nothing prevents you from seeing the light at point B if you're standing at point A. In contrast, if there's a bunch of fog (whether mundane or magical) between A and B, it may be harder (or even impossible) for you to see B from A.
(Note that this relies on a common-sense interpretation of nonmagical darkness - the rules don't draw such a distinction, presumably because they expect people to apply logic and common sense in understanding how regular darkness works.)
As such, a creature in the middle of the fog cloud would be unable to see a creature outside the cloud, just as the creature outside would be unable to see the creature within the cloud. If one attacked the other, the attacker's advantage from being unseen would be canceled out by their disadvantage from being unable to see their target.