An SEC reporting company has to “prepare” for an RS and it can’t just be done from scratch in a “few days”.
1st shareholder approval is required in most cases. For MULN they are seeking that shareholder approval now to allow the Board to trigger an RS in the future without having to go back to the shareholders.
2nd they will be required to file a Pre14A/C notifying the public of the intended corporate action and then
3rd they need to file a def14A/C no earlier than 10 days after the pre14c.
So all in all, between notice, shareholder vote, Board vote and the filing obligations it can indeed take “months”.
In the example you cite, AVCT, they filed their Pre14A on April 19, 2022, their def14A on May 2, 2022 and affected the stock split on October 3, 2022, so they were “preparing” almost 6 MONTHS before the RS.