Not really sure what you mean by True. Payload for a truck is on the sticker.
If you use the RAWR and FAWR, you’ll need to take the truck to a scale to know how much capacity each axle has. In practice, I think most of us would say you’ll be happier if you stay under the GVWR. Another issue with using axle ratings is that the tires also need to be able to handle that load which also means they have to be inflated to carry the weight.
I suggest shopping for a truck camper. Once you find the camper and know it’s weight, look for a truck that is sufficient to haul it. Unless you need a SRW, that usually means a DRW. Sure, you can haul a lot of camper on a SRW, but I bet you’ll enjoy the DRW more when you are fully loaded and bring all of your stuff plus have full holding tanks, etc.
I was able to get by with the SRW carrying my TC because I was very careful to minimize the amount of water and clothes etc that we carried. Not a lot of fun, but doable when I absolutely had to have a SRW.