Actually there's no incongruency.
The Normandy landings happened in June 1944, the atomic bombings in August 1945. Unless I'm forgetting The Wolverine stating Logan was a prisoner for a very long time, it's not unreasonable to think he could have been in both theaters.
It's certainly not explicitely explained, but time-wise, it's not physically impossible.
The actor you might have recognized is Hiroyuki Sanada, who in Endgame plays Akihiko, the only Yakuza who stays alive long enough for us to see his face. In The Wolverine, Sanada was playing Shingen Yashida, Mariko's father, who had more of a role already.
But apart from the fact that they're played by the same actor, there is no real ...