So here's my theories:
Headphone Actor:
The group of scientists(?) plot to destroy the never-ending world that Azami created. Not knowing how to accomplish this they plot to experiment with different things to try and destroy it. The first idea is to blow it up with bombs like in Headphone Actor. Unfortunately Enomoto got to the site where there were going to throw the bomb from too late. Somehow during this Ene tries to get her out of the city before it's blown up. When Enomoto gets to the scientists(?) they blow up the city much to her shock. Ene then apologizes as she was trying to get her past self to stop them. Konose is somehow at the same place trying to stop them as well. After Enomoto gets there the two team up to try and stop further experimentation on Azami's world. Their plan backfires on them. Konose is kept for further experiments after Enomoto escapes using her "opening eyes" ability.
Konoha's State of the World/Kagerou Days:
After they failed Azami steps in as the cat on August 15th when her powers were at their peak to try and accomplish what Enomoto and Konose couldn't. In the process she is found by Hiyori and Hibiya on their way to summer school. Though she wouldn't mind spending time with them she has to get back to her plan. After she starts walking away Hiyori and Hibiya follow. Unfortunately a truck driver slams into Hiyori. Everyone around them immediately "focuses" on Hiyori due to Hibiya unknowingly using his ability. Azami seeing this decides to try and save them and loops them back to August 14th in an attempt to save them. To make sure they get out alive Azami stays by Hiyori's side. Hibiya then explains his nightmare of her being slammed into by a truck as Azami decides that she needs to once again get back to her plan. As she leaves Hiyori once again chases after her. On this day the scientists(?) decided to try dropping thousands of iron poles from the sky to once again attempt to destroy the never-ending world. Hibiya notices this and once again unknowingly uses his "eye focusing" ability to bring it to everyones attention. The iron poles pierce through Hiyori much to Azami and Hibiya's dismay. Before Azami begins the time loop again Hiyori smiles thinking that she's saving Hibiya by dying for him. Hibiya eventually realizes that he and Hiyori are stuck in a time loop. Figuring that since Hiyori dies each and every time he comes to the conclusion that their endless torment will come to an end if he dies instead. So after Azami leaves and the chase begins Hibiya runs out in front of Hiyori and gets hit by the truck. Thinking that the time loop has ended he feels he could die happy. Unfortunately Azami begins the time-loop one more time. This time Hiyori realizes that even when Hibiya dies the time-loop still continues.
During the time loop the whole "laughing heat-haze" is Konoha in paralell laughing in fear while watching and commenting on the scientists(?) experiments unfolding again and again on Hibiya and Hiyori. He somehow escapes the facility he's being held at and resolves to try and save Hibiya and Hiyori from the time-loop somehow.