Alright, so I know shit for dick about logistics meaning I'll probably miss or get some things wrong but screw it:
Okay, so let's talk about the Gate itself. Things 52 meters tall and wide according to google so the biggest question one can ask here is how the fuck are the Imperials going to waltz in 100k men to invade before the jsdf or United States military comes knocking? It takes three hours to travel through the Gate on foot btw. Now I know the Romans were organized and Sadera is a cheap knockoff of them, but at best they're getting like a couple thousand men through the Gate every hour which when considering response time from our side means we'd realistically catch half their army lacking at most. That's not even accounting for horses and wyverns either. They would make things take even longer. They should know how long this would take, because they sent scouts who should have told them about this.
They also need food and lots of it if there are 100k of them. Hundreds of thousands of tons of food would need to cross the Gate every single day. Even a Saderan general who knows nothing about the modern world would completely understand that they are fucked if the Gate gets cut off from them. They had scouts pre invasion which should have and would have told them about how dense the city is if the Saderans weren't baby eating rapist evil ass isekai empire 383992.
Then there's formations which would quickly become impossible to maintain because Ginza is dense as shit. The Romans did actually do smaller group fighting in urban environments so they would have some concept of this, but not to the level of Tokyo, the third largest city in the world. Also, once again, Ginza is packed. Communication would be next to impossible. They should know how impossible this would be given they have fucking scouts who have eyes who should be of sound mind who would tell them how big and dense Ginza alone is just from one goddamned look.
Then there's water which they'd need hundreds of thousands of liters of per day to maintain their army. Horses and wyverns need a lot of that stuff. Where's the water Caesar? All I see is a goddamned concrete jungle. Now, maybe this isn't as bad because a mile or so away from the square there is a river which medieval armies would rely on for a water supply. Even still, what about beyond that? Sadera planned on capturing everything after all. We'd round back around to holding the Gate.
I don't mean to be a George RR Martin, but do you see what I'm talking about? Any realistic medieval general would sooner say "fuck that shit lmao."
Tldr: The Gate is a bottleneck and Sadera is stupid once again, who would've thunk it.