Is my battery dead

The voltage seems to be OK as long as it was left for a while after the charger was switched off/disconnected  before checking the voltage and why not just move it backward and forwards using your mover to see if it is OK  but most caravan fridges only work on 12 volts when connected to a tow car

But the fridge only runs off of battery if connected to your tug and it is running, e.g. car battery, never come across a fridge that runs off the 12v internal battery.

The fridge is not powered by the on board battery so unless you have a wiring/relay fault it will not have been the fridge which only runs on 12v when connected to the towing vehicle with the engine running.

What was the voltage before charging? A better indication of the state of the battery.

I, too, first thought the OP was erroneously saying the leisure battery was drained by the fridge motor but, on reflection, I believe he means he left the fridge set to battery after towing it home instead of turning it off.

If so, the live feed from the leisure battery to the fridge's control panel and interior light would still have been drawing power from the battery all the time the van was parked up.

I've never come across a low battery disconnect feature in a caravan.

"If so, the live feed from the leisure battery to the fridge's control panel and interior light would still have been drawing power from the battery all the time the van was parked up"

but surely this would have been miniscual amounts of power, its only an led control panel, and surely the interior light would be off if the door was closed ?

i suggest you try the mover, no need to engage the wheels just run it backwards and forwards if it spins round then all should be ok 

I think you will find he needs to engage  the rollers to put a load on the battery, this will draw a high current to test to it fully 

Was the door closed? What was the state of the battery before the event? These are all points to consider along with the fact the van has been left with the fridge turned on for 4 weeks. The OP wouldn’t be the first person to have flattened his battery in this way. Others have posted similarly in the past.

As far as we know, this was the only unusual draw on the battery. Have you a more feasible explanation?

I find the icon of a battery or '12V' on a fridge is misleading/confusing .... it'd be better having an icon of a car instead. There have been loads of posts here over the years where people think their fridge is being powered from the caravan's leisure battery.

The fact you left the fridge on battery means it would be connected nowhere at all. What that does it switch the fridge to be powered from the towing vehicle. If your battery went flat,the fridge was not the cause. It sounds to me as though your battery was fully charged at 13.16 volts. A fully charged battery at rest should show 12.8 volts, if you had left it to settle a while longer this may well have been the voltage you would have seen.

Like others suggest, to see if it holds the charge, use your mover.

peedee