A typical jam is an event where you create a game under restrictions. Using AI would trivialize most of those restrictions.
I copied a few random quotes from rules of actual jams, telling about their AI restrictions. And not all of them forbid AI. All jams have different rules.
So you see, the tools of the trade, code assist done with ai, are usually not forbidden. But a jam is a contest of art and using gen ai defeats the purpose. It is not a contest of who can operate the prompt best.
Also, most jams have the implicit rule, that since you would make the game for the jam, you actually cannot submit it to other such jams. It usually is also not quite possible to conform to different jam restrictions at once. Like, make the game in a week for the jam and include topics a, b and c.