Pumpkins mean "hey it's everything is flavored 'pumpkin spice' season again". It's right next to 'everything is hard apple cider flavor even if it's not hard alcohol' season and 'everything egg nog' season.
As someone who tried gardening a few years and did grow pumpkins I can add that it's AMAZING how far and wide a single plant can spread. Also yes they do climb onto things and you can grow them on trellises.
Are these supposed to be kabocha or unripe regular pumpkins? I have issues when people translate kabocha as pumpkin.
Kabocha pumpkins. I see the term "kabocha" applied to standard orange pumpkins all the time in Japanese, so for the sake of immediacy of humor, I treat them as equivalent unless there is a specific need to distinguish between them. Here, even if you don't know the difference, it doesn't make a difference to the punch line.
