Very nice development.
The dictatorship country had a lot of internal problems and the lucky encounter will just make them worse, they will waste resources on false paths to proceed a fake route.
I think that the country where the archmage reincarnated have no rights on his legacy, dude made very clear he wanted someone lucky or smart to get it.
Personally I dislike how we don't know how MC got to it, he simple discovered english was related to Lucas and the guy named some stuff after Earth big names, we don't know what MC actually found from the hints.
My guess is that to avoid casuality the archmage used english to give vague hints, but the real thing was in the stuff named after Hollywood and the likes, MC possibly searched for a locality name in the game that we in our world would react to it, in short, someone from our world would connect the docts, but someone from the isekai coulnd't even see them.
I'm sure someone thinks that is dumb how they dropped MC from the suspects fso fast, but they don't seem to know MC position in the country, they don't know he was forced to reveal himself and couldn't keep his original plan and get the all the lucky bonuses in the shadow.