Is it a foul when a player calls a wrong score in badminton?

The umpire (not the referee) is in charge of the scoring. Players can announce the score to their partner or even their opponents, but that is not binding in any way. It's hard to prove a negative, but you can peruse the official Laws of Badminton and won't find any mention of a fault of incorrect scoring.

The following laws could apply to a talking player:

§14.2.5 It shall be a fault if in play, a player deliberately distracts an opponent by any action such as shouting or making gestures;
§16.6.3 A player shall not behave in an offensive or inappropriate manner.
§16.6.4 A player shall not be guilty of misconduct not otherwise covered by the Laws of Badminton.

None of this applies: The shuttle wasn't even in play when the score was called, and it's neither offensive nor misconduct to make a mistake.

A case could be made if a player intentionally calls the wrong score all the time. However, even that would be dealt with by the umpire, not the opposing player. The umpire would show a yellow card (without any changes to the score) first. Awarding a point for a fault would be done by the umpire showing a red card, which requires serious misconduct.

Incorrect scoring by the players is no big deal: The umpire clearly announces the correct score after every rally. Usually there's some kind of scoreboard; at higher levels you'll find a TV at either end of the court displaying the current score in big letters. If the player thinks the umpire made a mistake, they can talk to the umpire before the start of the next rally.

However, the player who touched the shuttle did commit a fault:

§13.3.4 It shall be a fault if in play, the shuttle touches the person or dress of a player.

Therefore, the umpire will call out "Fault. 7-4." and update the scoreboard (if any) to 7-4.