Quick instructions I ran across from a prepper site years ago was that you could protect your stuff by using a metal trash can lined with cardboard-including the lid.
I use this to store a solar generator and various radio and electronic equipment. From my discussion with Marcella, she told me that my oxygen machine would be safe as long as it was not plugged. So Yes, disconnect battery.
If you have a shed house, maybe you should just put on a metal roof and sides or something - more durable than tinfoil.
It’s more doghouse size than shed size. Battery is usually inside the shop (converted barn, block on the ground floor, spruce upstairs and metal roof)), being trickle charged or waiting to to be used. Afraid foiling the outside would be a waste of time with weather effects, plus maybe intensify the sun’s heat in the summer. so I was thinking of foiling the inside. Thought about foamcore covered with foil and cut to fit. It does have an electric start, hence the battery. It runs on gas....we buy premium for storage and add 2x the Sta-bil.