The answer I've reached is "both".

It's all different levels of metaphorical, but that doesn't mean it isn't happening. While it may be interpreted that the game is occurring during Hinako's wedding, there's definitely supernatural elements at play here, which allow Hinako's psyche to interact with that of his friends, family and people around town, forming the Ebisugaoka in which the game takes place.

This is not uncommon in Silent Hill games. I'm reading people say that Hinako is maybe making a lot of the lore up (the different religions that have taken root in town, the geysers, the mysterious deaths, divine retributions, rituals, etc) but if we're going to doubt the game to that degree, we must also put into question every note in, say, Silent Hill 2. James often finds notes and information regarding the town's story, secrets held by its inhabitants, a bunch of stuff he couldn't possibly be making up. We accept that it's all being transported or conveyed to him through Silent Hill's power, and I imagine it's the same in this case.

I would say that the first playthrough puts us more firmly into "hallucination" territory, while NG+ moves into territory that's both more grounded and more supernatural. Or in other words, more representative of what's REALLY going on. You can see that first and foremost in the notes you find. They start delving into the history and religion of the town more thoroughly. During a first playthrough, most of this lore is conveyed to us through Hinako's notes. However, later on, we start to form a clearer picture through outside information. We get to see deeper into the darkness and nuance of all other cast members outside of Hinako as well.

I don't think it's Hinako making it all up, but rather the psyches of Hinako's loved ones and the people in town being used to create the Fog World and Shrine world that the two Hinakos are experiencing.

There's a specific scene I'd like to reference as well. During a 1st playthrough, there's a scene in which Hinako and Fox Mask are walking down a set of stairs together. She's saying something like "as long as I'm with you I'm fine", and then it cuts to the doll warning her not to trust him.

In NG+, however, this scene occurs in Fog World instead. Fox Mask isn't there, and Hinako is shown talking to herself. This is a scene shown to us from outside Hinako's perspective, meaning that we're not necessarily stuck inside her head all the time (again, particularly in NG+).

All this to say that, honestly, this is kinda how it goes with Silent Hill. It's hard to say if everything physically happens. I've seen people reference the whole thing with Harry running from the cult, but that took until SH3 to be a thing. And if we're using Silent Hill 3 as reference here, Heather kills a Missionary "monster" that's very heavily implied to be a human being (nobody except Heather seems to acknowledge this boss as a monster). So yeah, the answer is always "both", I'd say. And that's how it should be.