I believe there's a decent camp of people that think the space war isn't real, and that it is literally a gag and/or a completely random way to have an (almost) all-female setting.
If you want to rationalize it, there's a few ways you could at least attempt to. You could start by saying that generally, military tech is 10-15 years ahead of civilian/commonplace technology. You could further this by speculating that most government research funds went towards space exploration, terraforming and/or rocket technology — either before, because of, or even more-so because of worrying discoveries or alien contact. Kumon-Mi is also "outside Tokyo" (IIRC,) but we're not given much else about its economy, geography, culture, etc., or shown anywhere else. It's possible that Tokyo is partially on its way to Cyberpunk 2077, alongside places like Washington DC or Amsterdam, but Kumon-mi is not one of those leading cities when it comes to growth and economy. It might not even be Japan providing this technology in the first place, it could all be NATO or US space-faring tech, especially with their restrictions on military spending and size post WW2. Basically, Kumon-mi is a more traditional / middle-class city as opposed to a Silicon Valley, and Japan isn't on the technological forefront anyway. There's quite a difference in economy and infrastructure in Kumon-mi itself, with the old district. Considering that nearly ALL men have been drafted, this war is clearly a huge deal, and a similar thing is happening here to what happened in the world wars, where production and resources are going straight to the war, and all innovation is focused therein. Also, on the subject of the barrier, it is essentially just a big ass wall that's likely well guarded and controlled, but it could work.
In summary, Kumon-Mi is a fairly average/middle class city (with a 'poor' area) that wouldn't be modernized like Tokyo, in a country likely not on the forefront of space-faring technology, and was likely walled off near the start of the war, while production was ramping up. For whatever reason, the US, China, or whoever else was probably already investing in space travel, or even started work on colonization. Most technological innovation, funding, and resources are being concentrated solely on the war — and most of this is probably concentrated on space travel. Most countries' economies are probably being crippled because of this already. A war like that is unprecedented, and even in America in WW1/WW2 basic items and materials like metals were scarce, let alone tech.
Does the space war make sense now? I don't know, probably not. Maybe. Although if one did happen right now, in real life, it'd probably lead to a great depression worldwide on Earth, so it might be more forgivable than it seems at first.
