I'm a camp host that has several tent sites at the campgrounds that I take care of. I don't give two squirts how you sleep as long as you paid and are courteous to the other campers. However, if there is only one tent site left while other non-tent sites are available and another camper with an actual tent wants to stay there, I would see that that camper with the tent got the tent site with you going to another site. If that was the only site left, I would let you share my site as there is plenty of room for a van. Probably even give you half off for putting up with my crap. (I'm really annoying.)
Putting a cooler and a towel or whatever campy-type-thing you have on the picnic table works great to hold a site. Just a couple of items works great for me. I don't like to see a messy camp, though. Too much would be overkill. Just a couple of items to say, "Hey, I'm not gone yet. Just out hiking or fishing. Be back in a bit!" That will keep other potential campers out. If you rely on just the tab off of the envelope one the numbered post when you paid, it might not be enough to keep potential campers out of the site.
You could cordon it off with velvet rope or several orange cones.
It's quite rare for someone to steal something in most camping areas. If you are concerned with that, a ratty, old towel and a broken flashlight would work. Make sure the colors are bright so the camp host and others can easily see them on the table. If the table isn't visible from the road, something like a chair with a cooler beside it where it is visible would also work. I've seen a camper leave a fire unattended with a full garbage sack under the table in an area with bears and a food storage order in effect. Clearly, the site was occupied, but I don't recommend that.