Sometimes, just finding the right keywords... on the off chance I got the soft drink name right, I searched for taylor lung ramune and got a link to one of the chapters of "Go Gently", a crossover between Worm and Welcome to Night Vale. Taylor knows Lung as Mr. Eikawa.
Case and point; on my way back up, I was called over by Mrs. Yamaguchi from the six floor, holding a flimsy cardboard package of six glass bottles filled with what seemed to be a pale pink soda. "Oh, is your friend already gone?" The portly woman asked, a little dismayed. "There was a sale, so I thought you two might like to try some. I suppose you'll just have to work through it on your own." She tossed in a wink.
"What is it?" I asked, trying to pick out some sort of label I could recognize. I saw a cartoon peach on the corner, which cleared up the matter of flavoring, but the actual name escaped me.
"It's called Ramune," Mrs. Yamaguchi told me. "It's a popular brand of soda that started in Japan."
....
I furrowed my brow in consternation. It was...a strange cap, it seemed, with a weird protrusion on the inside and perforation around the top. The mouth of the bottle was smoothed over with another bizarre cap, made of rounded plastic and embedded with what seemed to be a glass marble.
I heard a faint noise, and when I looked up I saw Mr. Eikawa already leaning on his balcony, in his customary long sleeves and with a towel slung around his neck. He seemed even more intense than usual, so I kept my normal greeting to a quiet mumble and reapplied myself to the apparently Herculean effort of opening my Ramune bottle.
The cap wouldn't pull off. The marble, when I pushed at it with my thumbs, wouldn't give even a little bit. It wouldn't roll like a ball-point either, when I ran it across my palm, I had twisted at it both clockwise and counterclockwise, and was about to throw my tattered dignity to the wind and resort to biting at it when I heard another sound. I almost didn't believe it, but when I looked up...
Mr. Eikawa's shoulders were shaking. It was a slight movement and utterly silent, aside from the initial snort of amusement, but he was actually laughing at me and my ineptitude.
The general setup for how they wind up there is that Danny's depression is worse and he decides to commit suicide while Taylor is out of the house on a sleepover. That leads to his Trigger event which gives him some vaguely defined powers that cause matter he touches to go mushy, which inadvertently leads to the house collapsing around him before he gets control over the power. The apartment building was convenient, and he shortly thereafter winds up working for the Protectorate, eventually transferring to Boston. Emma triggers during an ABB gang attack (the attack is much like canon, but the entire Wards show up instead of just Shadow Stalker and she Triggers) and joins the Wards as Cadenza alongside Shadow Stalker, unbeknownst to Taylor, which leads to a more cordial relationship with Sophia.
One last unresolved thing from the question, Taylor does trigger after a scenario where a bully tries to reclaim his reputation to get a chance at a gang initiation by ambushing her, tying her up, and dumping her into the bay, where she drowns before being rescued by the Wards, getting a grab-bag of powers that basically turn her into the radio guy from Welcome to Night Vale. The fic went on hiatus before it could explain things further, but she basically has Tinker powers that let her do pirate radio at will and either gives her a greater insight into the weirdness infecting the city, which she reports on via her broadcast, or gives her powers that cause that weirdness.
