[UPD] Solution: the guides don't mention that, but you have to complete Inazuma main quest to get access to it. When you complete the main quest and get directions to Sumeru, talk to the shrine maiden, fast-forward time to tomorrow morning (! tomorrow is important!) and go to the teleporter near Adventurers Guild in Inazuma. I hope this helps someone if they are as stuck as me.
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So, I completed all Grand Narukami Shrine missions, visited the secret hideout, got the "SYUUMATSU GAIDEN" achievement, but the following chain of quests is not starting. What I did:
- visited Narukami Shrine and talked to Gendou impostor again
- shifted time to the next morning
- teleported to Inazuma Adventurers Guild
...aaaand nothing happens there.
I've also tried getting new fortune slips (without a hazy night), waiting for the server reset, shifting time more than 1 day ahead, but nothing helped.
(AR 46, so no problem with low AR)
Either I'm missing something, or the game is glitching. Help, anybody? It's been 3 days since I had found this issue, and I'm our of my wits.

