While I love the lore, the problem is that notion that outhouses historically had crescent moons cutouts on them is not supported by history. This idea became popular in the 20th century in comics, cartoons, and other humor-based media (and seemed rather quaint since toilets were widely used in the 20th centruy) . Some historical sites then retroactively put credent moons cutouts in the doors or walls, due to tourists' expectations, though not all historic sites did this.
Cutouts would be used for light and ventilation, and sometimes in place of a door handle (probably a simple round hole for this case), but many of those were usually in the rafters, unless used as a door handle, and they weren't necessarily used as decoration, but there were some instances where they would use shapes like a "diamonds, V's, or heart-shaped" cutouts on the doors.
The reason for the use of the moon to denote an outhouse starting in the 20th century was most likely because in comics or cartoons it was a way to signify that this building wasn't a tool shed or something similar, but instead was used as a toilet, since most children wouldn't have used an outhouse. The moon was used because by the 20th century the slang of "mooning someone" was in common use for when people would jokingly drop their pants and stick their rear-ends out at others as a prank. The moon then started being used in comic media to signify that this little building was where one would drop their pants to go to the bathroom!
However, that doesn't mean that in this upcoming pack we can't imagine the moon in the game's outhouse being related to a girl's outhouse, the Roman goddess Luna, or having to do with fairies magically whisking the mess away. 😉