IMO Lucy from the Grandchester Mystery Mansion and the Dunwich  flashbacks and events in fallout 3, 4 and 76 are the best evidence of paranormal activity.

What if the Stranger is a title, like The Phantom in comic books. It's a position passed on from person to person. Like a secret vigilante society or something.

If you listen closely you can hear 5 tons of power armor coming down the hallway.

I love how weird and creepy fallout can be.

At least it’s not a Ghost Deathclaw.

I believe that the Mother of Fog is actually Moira from Fallout 3. What brought me to this conclusion is three key things I notice while playing through far harbor. First was the voice, both the dialog and the laughter were almost identical to 3's voice except a bit older and distorted. Second was the character model used same body type and hair style. The third is the personality of Moira, what more of an interesting subject to study for the rest of your life then the people who worship radiation to the point of poisoning themselves willingly.

According to google there are also those sounds from the goodsprings cemetery in Camp forlorn hope and bitter spring

The real ghost was the update we found along the way

"Corpureal" is a valiant attempt. 😁

I think ghosts being in the game makes sense. The absoloute devestation of the war and life after it would leave behind so much negativity and just the feeling of loss.

To be fair on the physics here, I think the fact that the land is irradiated, and nuclear waste definitely has an energy signature, probably causes them to simply manifest differently as a result. Ghosts rely on the human energy to boost theirs enough to do...anything. demons don't,  because they have their own power without a corporeal body. But it also goes, in this universe, that you don't need to be a psychic or psycher to see or hear a ghost. It seems like the universe of Fallout references the emphasized energy signal of the leftover nuclear radiation with the bone phantoms. Though I think with the Grandchester mansion, they just wanted to stick as many of the paranormal show references: Addams family, the sixth sense, rosemary's baby, poltergeist.
And to address the Mysterious stranger: look up the concept of a Tulpa. They are usually an intentional manifestation of ones mind during certain catholic rituals.  The only real difference between them and what a poltergeist is would be the intention. And this could work out for the stranger for three reasons: first, The Nuclear energy signature of the wasteland may be the cause of the tulpa  manifesting a bit more corporeally, to the point of others being able to see him. Nick is a synth, but that doesnt mean his energy sensors don't pick up the energy anomaly. What he sees may be completely different to what you see-kinda routes to the logic that you may see red as a specific shade, but someone may know it to look differently.
Second, the Stranger looks at least a little different in every single incarnation of the Fallout. In some, he has a mustache, in most, he doesn't. What if this is a result of the varying interpretations of what this particular trait is supposed to be? This would not make them a psycher, as it's their own energy they're registering.  Tulpas were meant to aid in one's Religious tasks and rituals, though they're supposed to be let go of once those are done, else they could wind up bring more poltergeist like.
Thirdly, he comes to aid in times when you most need it. When YOU most need it, and the frequency of  his appearance depends wholly on your luck? He is literally a trait you can choose when you reach a certain skill level. It's specific people manifesting him, no one else.
That's my theory; he is a manifestation you can sometimes, depending on your luck-which, to emphasize my point, dictates your speech check success in conversation-manage to score. As your luck level goes higher, so does his appearances. The different levels of the Stranger perk merely changes, in small measure, the effects of the manifestation. And yes, Nick can pick up that mental projection. Which implies your manifesting skills are off the charts. Or just boosted by the nuclear waste energy around the wasteland.

Not me sitting here thinking about all the dead fly ghosts and just imagining hearing a constant ghostly buzzing noise.  I'd lose my mind.

I could be crazy but Anna Winslow might be a reference to Dianna Windsor both by name and an odd death

Given it's supposed to be a haunted house? They probably had designed all kinds of secret passages so an actor playing a ghost of little Lucy could appear and disappear and scare guests. I always figured a young girl was living in the mansion and using those passages. Maybe even a child ghoul (which are also canon in Fallout 4 thanks to Billy and the fridge) who's gone crazy and thinks they're the ghost of Lucy?

As for the actual appearance of the child and the various mechanics? I think that's probably due to Bethesda trying to make it spooky while leaving it open as to who the girl is and how she's getting around the place (or if she's a ghost or not). Bethesda does like to leave their options open and let players fill in the blanks, after all.

The supernatural aspect of Fallout is my favorite thing about this franchise. I truly hope we get some of that in the show at some point (idc if it’s a main plot point or just a throwaway subplot)

Watching this, I had a thought about the Mysterious Stranger. When he appears he has a distinct appearance, but he also looks somewhat similar to Nick Valentine. If the Mysterious Stranger was actually a spirit, could it be possible that he is the spirit of the detective that Nick Valentine is based on? It would explain why the Mysterious Stranger always randomly appears to help the "hero" in his fights and why Nick Valentine is so obsessed with tracking him down.

Well, it's also possible that the flashes we get at Dunwich Borers are the memories of the ghouls that are being projected into the Sole Survivor's mind... somehow? IDK, insert weird psychic experience.

Hmm, what if the Mysterious Stranger found an alien or eldritch artifact that extended their life indefinitely, but also made them intangible. They're only able to become tangible/visible/able to interact with the real world when they act to protect others.

Honestly a interesting note about the Mysterious Stranger is that BGS changed his appearance between Fallout 4 and 76, unlike 3 and NV sharing the same model, implying there is some linear progression to whatever he is.
Tho personally I did like Amazingly Awesome Tales 8 concept of him being a time traveler.

I love anything to do with Dunwich.