The pure and honest Shameimaru here!I'll let you guys know about anything you want!
Established on this day because of the month Fumidzuki (7th month) and because it's letter-writing day (23)!
This one hinges entirely on the 文 kanji, which is both how Aya's given name is written and the "bun(s)" in "Bunbunmaru".
The seventh month of the old Japanese lunar calendar was known as Fumidzuki and was written with that kanji (文月) and that gives you July (the seventh month of the Gregorian calendar).
As for the day, the way this was written seems to make a reference to fumi no hi (which I guess roughly could be translated as "letter-writing day", which is another Japanese commemorative day. The "fumi" in "fumi no hi" can also be written with a 文.
As to why fumi no hi was set on the 23rd specifically, that's a pun: fumi → fu + mi → 2+3 → 23.
