If you are car/truck camping a Jackery or equivalent works great. I did the TAT on a KLR 650 using a Jackery, took some extra work but was worth it. Hiking, well even light batteries are heavy. I am lucky enough I can sleep on my side in a hammock and not need my CPAP. Charging the battery will be a big hurdle. Figure out how much power you need per night, how often you can charge (I rigged an power outlet on my KLR, worked great but DO NOT leave it charging unless the engine is running. kill the bike battery and starting it is a bitch). I have done about 270 miles on the AT. Maybe others can figure a way to deal with the battery problems but I couldn't. Even small solar panels add eight and don't do well unless laid out facing the sun. Hard to do while walking.
I did come up with one sneaky idea that could have helped. Carry a three outlet adapter so if you run across an old soda machine or whatever you can slip that adapter in there and charge without shutting off the machine. I know, not exactly ethical and I never did it but it was an option presented to me.
ETA, Your CPAP power consumption can vary. Mine runs 15" and uses a lot more than those tuned lower. A Jackery 240 is good for about 1 1/2 nights.
Car/truck camping where you do not want to start your vehicle to charge can use solar panels to keep batteries charged.
How much weight can you carry determines a lot of your strategy.
With 120AC CPAPs a kill-a-watt meter works great for determining power needed. 12V DC can use an inline power meter. The resulting math is too hard.
LOL!!! Holey thread resurrection and I have already chimed in here. Oops...