Just a quick update, I left my cookies overnight and went to purchase them just now. After they were opened the timer is saying restock in 1hr 5min, so I can finally confirm 100% that we absolutely only get two cookies every 24hr hours and they will not change again until 11am regardless of if you buy them or not. The timer is not dictated by the time you purchase the cookies but by the daily cookie switch at 11am (EST). Basically, if you buy cookies as soon as they are available you will have a 24hr cooldown, but if you wait until 10am (EST) you will only have a one hour cooldown. That confirms that there is zero reason not to buy the available cookies even if they aren't special character cookies, unless you are very low on bells and need to save them for the special character cookies, which cost 5k each.
Now, as for the tweet that said 12hr update, it was either a typo that Nintendo has yet to address (and they really need to because the community is very confused) or the game is not working as intended, and they are working on a fix behind the scenes. Theoretically Nintendo will provide a gift if the latter is true, but I'm not counting on it. I honestly think someone put the wrong info in the tweet, and Nintendo is working on how to communicate that without upsetting the community.