Neither...
It's their birthday today, and we know the date. Surely it's some form of the date? But none seem to work.
Yay, thank you! I'd actually tried a lot of codes like that, but I think the extra complication of American / European date formats meant I'd missed that exact one. Still, now that I can play the game it's really fun!
Very short, obviously, but lots of potential. It reminds me of Strange Horticulture, if you know it.
Ah--somehow I parsed "November 15" as today's date (which is a thing a lot of computers-within-computer-games do), and didn't particularly parse the birthday hat as "today is my birthday". (It's an old decoration? They came from the break room where there was cake for a coworker's birthday? Anyway.)