There's something you see very often in stories that start with an implausible premise like this: how do you communicate the strangeness of your situation to other people and have them believe you? Whether you're dumped into another world, tossed back through time, inheritor of ancient magicks, you're left keeping a secret from everyone around you simply because nobody would believe you if you tried to convince them.
Often, this is where that line of thought ends. The protagonist simply keeps their secret close to their chest, even after becoming close to people. They have a plausible fake story by now, maybe handed to them by other people who guessed based on available information, and they don't feel any urge to correct the misunderstanding.
It's horribly lonely to watch.
Imagine if Hazou hadn't opened up here, if he hadn't steeled his resolve and put his faith in Mori and Wakahisa. He might lead them with supernatural intuition and impossible insight. He might help them overcome threats within and without, and guide them to a happy life working to save the world. But every step along the way, he would be second-guessing his actions. Mori and Wakahisa would have their own theories for why Hazou has this knowledge, and Hazou's every action would have to be compared against those theories for fear of inconsistencies. He wouldn't be able to speak what's really on his mind because so often it'll be related to context he can't share lest he reveal the lie.
And the lie would build on itself, solidifying with every action he takes to reinforce it and every moment he allows it to continue. If it's hard to come clean initially, it's much harder to come clean after spending months or years deceiving them. They might rightly ask if Hazou saw them as little more than tools to be guided and manipulated. Mori especially, since we know how much Kei values her agency.
Many stories are content with the double life, with the protagonist having nobody they can truly trust and rely on, but that makes it all the more valuable to me when I see a story that refuses to take the easy way out. There are so many interesting and novel plot developments you can do when the main cast all knows the truth that you can't do at all when the protagonist is keeping up a cover story, and on top of it you get these moments of intense emotional release where it's like the world opens up and settles into a new configuration. I absolutely adore when a story has the strength to take this route and show genuine trust between the main cast, even when it's hard.