2002 is definitively wrong and has been corrected to 2006.

But, do you have an official proof that this episode has been broadcasted on September 22 ? Every site I look at have it on September 29, one week after "New Leaf" : Fandom, SBMania, Wikipedia.

Best proof I have is that Paramount+ lists the episodes together, as they are sister episodes where 2 11 minute episode air in a 30 minute block, and it has the date as September 29, 2006, which doesn't sound wrong, but does change the date for "New Leaf".

I'm not sure what's going on on the Wikis. There's a chance that Nickelodeon premiered these episodes outside of a proper SpongeBob block and only aired them as a single episode, like after a movie ended, but I can't find proof of that, and the wikis don't have citations on where they got their dates.

On Fandom, the 2 episodes are listed at the same airtime of 7:30pm. So, it's possible that they have been broadcasted separately.