BETAverse vs EXTRAverse
BETAverse
The BETAverse is the current setting, though it is never directly called the "BETAverse". It is an alternate reality on Earth, loosely based on our own, though with major divergences in history and, most glaringly of course: the existence of the BETA and the ongoing war against them.
Because of political turmoil and an alien invasion, many factors affect the people within the world. Through decades of attrition, many schools have shifted curiculum towards warfighting and survival, men are noticeably fewer in number as they were the first to be drafted, slowly dwindling in numbers over 30 years. Older men that remain are either too injured to continue to fight and have since moved into leadership roles, or serve as technicians, mechanics, and scientific personnel. The ongoing situation has spiraled to the point where 16 year olds are enlisted in probationary cadet roles, and in more desparate contries, conscription has dropped as low as age 14 if the child in question is an orphan. Compared to real world population figures, over half of Humanity is already gone. Roughly 2.5 billion people remain.
Years of war has prevented recreational or luxury product revolutions, video games are a foreign concept and the internet is used exclusively by Earth's militaries for datalinking, communications, data storage, and realtime battlemapping. Social games like cards, chess, shogi, marbles, or cat's cradle are considered adequate recreation in this setting. Civilians get their news through papers or television, which is heavily censored and propagandized. Pets are considered too expensive to keep as food shortages ravage the world; whole species of wildlife are now extinct from the endless march of the BETA hordes. It is, at it's core, an existentially grimdark setting.
EXTRAverse
The EXTRAverse, while never explicitly referred to as such, is the mirrored reality for our own within the setting. It is both the real world and not, as within the context of the story, it is the relatively peaceful reality that @Takeru Shirogane is originally from. This reality, while mirroring the real, out of game world, is still a fictitious reality as various companies, politicians, celebrities, etc., are all altered in some manner or fashion. History reflects real world history, though individual names and participants may be obscure outside of national involvement.
In the EXTRAverse, children still go to schools with a focus on general education, they have time for recreational persuits and activities, things like the internet, amusement parks, and video games are all easily available to the standard citizen. Conflict between human beings are still a regular occurance, but usually far removed and regulated to areas historically known for conflict like the middle east. The world's population reflects real world statistics, roughly around 7 billion, and the mundane day-to-day struggles of maintaining a job, or a relationship, are usually the highest level of conflict an individual would see regularly.
Why is this important?
There may be opportunities within the story to travel between worlds or dimensions, though in the context of the BETAverse, this would be extremely resource heavy, requiring specialized equipment and knowledge. On top of this, travel would only sustainable for limited time before pulling the traveler back.
A primary example would be traveling to the EXTRAverse to converse with that reality's version of Yuuko Kouzuki to assist with the problems of the BETAverse's @Yuuko Kouzuki and @Alternative IV. Such an event would be a microcosm to the story at large, but during time in the EXTRAverse, there would be no BETA and no majorly destroyed cities. Theoretically, it could even be possible to travel to locations that would otherwise be gone in the BETAverse, like Germany or Isreal.
Secondary to this, @Takeru Shirogane's existence as a causality conductor is most visible during segments between the two universes. Despite originating from the EXTRAverse, he's become tied to the BETAverse; the longer he stays in the EXTRAverse, he unintentionally and uncontrollably siphons the memories of his former friends there back into the versions of themselves in the BETAverse, leaving these peaceful versions clueless as to who he is and planting their memories into the minds of their BETAverse counterparts that never experienced these memories themselves. If left unchecked, as the foci of information exchange between the two universes, Takeru's prolonged stay in the EXTRAverse could trigger a global calamity killing off every 3-in-4 people to force an equillibrium on the population as the two universes struggle to be one.
The science around the idea of a "causality conductor" is heavily theoretical, but grounded in quantum mechanics, physics and multiverse theory. Whatever entity serving as the conductor becomes a bridge, serving as a throughput between realities, exchanging causality information between them. Cause and effect information. So, while an end-stage effect may transfer over, the cause to attain that result may be different. Heavily oversimplifying, it is basically: "because it happened in a parallel reality, it happened here."