I am not expert in the specific subject, but. If the propane system fittings are to specifications then having the battery in proximity should be fine. The battery and associated electrical fittings need to be properly secure. Sparking and arcing are the concern. All electrical connections must be tight. Have a cover over the positive battery terminal or have the battery in a box so there is no possibility of the positive and negative terminals being shorted to each other or the positive terminal being shorted to nearby negative connections. I assume the manufacturer has done these things.
I assume that the compartment is not terribly airtight. But always make sure you secure the propane connections well. I think that after replacing the tank, opening and closing the big door a couple of times will flush out any small amount of propane that might be in there from the swap, sort of fan it out.
This situation is common in trailers and propane powered vehicles. The gas can be in proximity to the electrical system. But making sure you have connected the tank securely and that any nearby electrical stuff is proper condition will be good.
Don’t be stuffing a bunch of random stuff in the area that might cause sparking across electrical stuff. But again, the manufacturer should have that stuff protected.
Well now that I watched the video…
Put a protective cover over the battery. The manufacturer did not protect the battery connections. I thought the system was in that big back hatch area. At least get the positive battery connection covered. A battery box would be good. But if the battery connectors are tight and propane connections tight, all should be good.
But definitely protect those battery connections!!! Cover it up.
There will certainly be holes in the floor of the compartment to allow any gas leak to escape. The gas tank and the battery must also be secured in place.
One problem with this arrangement, especially in such a small trailer, is that the compartment becomes extra storage space which might block the vents and possibly short the battery connections.