Indeed, but we have also talked about how "shed style" buildings under 144 sq ft do not need a permit.
So we wouldn't necessarily have a permit specifically for a photo booth.
At least not for the structure itself.
They would need a permit to run the electric to it, but presumably that could easily come later in the process.
It’s likely that if a photo booth is in the plans, specific details of how much power is needed could wait til much later.
You could be right and they may not have a photo booth. But the lack of one in the permits is not a clear indication that it won’t happen.