@Ovnidemon I don't think your interpretation of the manga is the same vibe that I get from the manga. If you substituted Japan for any other country in our world, or with a fictional country, I don't think you'd say the same thing, so I think the bias about Japan's actions in WWII might be influencing your interpretation. But the manga is missing a lot of details that the web novel has, so it may not be clear as to what's going on in the story if you only read the manga. The Japanese military is superior in this alternate world which is why you'll see so much slaughter. Any other country in our modern world would appear just as strong if they were transported to the same alternate world. The less technologically advanced native inhabitants will obviously be surprised on first sight of the destructiveness of modern weaponry, but I don't see any "boasting or bragging" of Japanese strength in either the manga or the web novel. The opposite is true (later on), where the lack of display of their military might causes misunderstandings with hostile nations into wrongly thinking that Japan was weak, which leads into conflict and creates all the nice and juicy war between countries with greatly different military power that we're all craving for, but I won't spoil further details.
There was a legitimate reason for the use of force in the early chapters so far, although the manga doesn't go into great detail. The web novel explains that Japan imports a lot of food and resources, and as the supply has been cut off from the original world, they have to establish diplomatic relations with the neighboring countries to find alternative sources. They've got 120 million people to feed and supply fossil fuels to. The first nation that they contacted, agreed to supply all of the food that Japan needed. Another one supplies all of their petroleum. But another less self-sufficient neighboring nation decided to invade those countries to take over the food and resources for themselves. They were also racists and used ethnic cleansing against demi-humans. So to protect Japanese interests (resources) they use this and other excuses to get involved with the conflict by kind of twisting the interpretation of the Japanese constitution, which prohibits the use of military force in other countries' domestic affairs, in order to allow them to do so. I don't see how Japan's past actions in WWII would have anything to do with this except for the part about the Japanese constitution, because any other country in our world would do exactly the same things that Japan did in this story if they were put in the same situation, which is to secure new sources of supplies and defend them in order to survive in the new world. The use of force to stop ethnic cleansing is also pretty common in our modern world with the use of UN peacekeeping troops where several countries commit their own troops to enforce, but I think Japan's constitution usually prohibits the use of combat troops for peacekeeping.
What you may see as "sparing lives" and "humanitarian" is instead what I see as normal rules of engagement. In the first naval battle, Japanese ships rescue the shipwrecked enemy sailors, which is a requirement of international law (well, from the old world), so I don't see anything specifically as propaganda from this behavior. Any other country from our world would be expected to do the same if they were to morally adhere to international law. In the first land battle, they rescued elf villagers from the attacking enemy cavalry. I also don't think this is propaganda, it's just a common way for fictional works to generate some heroism. If civilians were attacked in any other fictional scenario, I think you'd wish someone would come and save them. The part where the villagers see the Japanese rescuers as angels of the gods has more to do with a mythological background arc, which the web novel explains in more detail, but I won't spoil it.
However, there is a part very far into the web novel, which you probably won't see in the manga for several more years (at the pace that the manga is going), where a Japanese soldier makes a command that I found incredibly immoral ( didn't "try to make the enemies surrender at all cost", more like murder), but the author did not expand upon or address it further, and let it slip away.
Anyway, I recommend reading the web novel if you want to see the story with a deeper explanation of what's going on. The manga can't go into great detail because of the limited space and format. Mob of Deer has translated 1/3 of the web novel so far. The remaining chapters I read using Google Translate, which was difficult, but still understandable and interesting. I would say that Summoning Japan (at least the web novel) is much less propagandist than the Gate anime. Summoning Japan (WN) does a pretty believable job of showing what a country might do if it were suddenly transported to a hostile alternate world. I really found the grand scale of the world building and the exploration of the uncharted seas to be very exciting. And oh yes, the incredible slaughter from the difference in military power.