Is it customary for delivery van drivers, to permanently have a large plush toy in the passenger seat?

I’ve never seen that. I have seen a few garbage trucks with a stuffed toy on the front grill as a mascot.

Not that I know of. Have you seen that more than once? Do you have HOV lanes where you live?

I’m not a delivery driver, but when I moved halfway cross country I bought a box truck to move my stuff. My daughter sat in the passenger seat, but some previous owner had installed a third seat in the center. That was occupied by a three foot tall Elmo. That was six years ago. Maybe it caught on.
It really freaked out a couple of drunk girls who walked by when I stopped for gas.

@JLeslie Do you have HOV lanes where you live?

I do. People have actually tried using mannequins and blow-up dolls, and it’s always newsworthy when they’re caught. Anyone with that much audacity likely doesn’t embarrass very easily.

It wasn’t customary for the drivers of the delivery company where I used to work; however, it might be an attempt to make it appear that there are more people in the van than just the driver in hope of deterring a robbery, or using the HOV lane during rush hour, or making a cop think there are children in the vehicle & not stop them. People tend to look but not see so a stuffed critter could be misconstrued to be another person.