I've heard from other touring people I spoke to that they carry about a 1/2 a day of extra water just in case, and they are aways stopping to refill even if only one bottle is empty. I carry currently about 176 ounces of water, that is the water I start out with and it lasts all day and into the morning the following day and into mid day, but for backup I put 2 store bought plastic water bottles in my panniers, just in case, and I have that filter. But I always plan the trips so that I will be near water. I'm sort of at a loss myself if I was out in the desert and it took 3 days to find water! Ouch! But I would think with prudent route planning that shouldn't become a problem.
I carry the filter because I know people who have done extreme backpacking and bike camping and they all recommended having one just in case.
In the desert you have to learn survival skills to find water, which I'm admittedly not really good at, but they do have stuff on the internet that one should research if they know they're going to be in that situation. I think if I were about to head into that sort of situation, I would start out by stocking up on water, yes water is heavy but so is carrying out a dead body! So, I would probably put 4 store bought plastic bottles of water in the bottom of each pannier, so that would be 8 bottles, with two more going into each of my handlebar bag bottle holders, a lot more weight but as one person said you would be going through the water and eventually losing that weight. But using survival skills to find water in a desert is a last-ditch effort to stay alive, and what water you do find, especially during the dry seasons, is scant to none! you might get a few drops from certain plants, but not enough to sustain you for a day, and digging into the desert sand near a plant will yield nothing.
I don't like carrying a Camelback so I probably wouldn't do that, since that will make your back not only tired but hot. I have one of those, a small 70-ounce version I used when I lived in the Mojave Desert of Calif, but I never liked it except for it carrying the extra water I needed, but I didn't have a touring bike back then so I relied on by two water bottles that the bike could carry plus the Camelback. Now my touring bike can carry 5 bottles on the frame and fork, I use those Arundel bottle holders and can carry 4 32-ounce bottles, plus the underside of the down tube can carry a 16-ounce bottle. Plus, the two 16.9-ounce store bought water bottles.
I sort of mislead in my earlier post, my Arundel bottle cages can carry up to about 41-ounce bottles, I don't have any 41-ounce bottles, I only have 4 32-ounce bottles and one 16-ounce bottle I use on my camping trips, those are insulated steel bottles too so I don't have hot water to drink an hour or two into a ride. The bottles are kind of heavy but I was willing to pay for the weight penalty to avoid hot water.
I went bike camping all that year of the covid shut down, and I was able to find water. I went into a McDonalds that had the drive thru only open, and rode the bike up to the drive thru and they gave me a large water with ice for free and I filled up an empty bottle with it that I had finished off during the ride up to that point. Gas stations with mini marts stayed open too so they could sell gas, they had water not only in bottles but at the fountains and even outside spigots could be used if necessary, in addition to plenty of ice and other assorted drinks in the fridges. the state parks had their stores open and they had water, other drinks, not to mention water at the spigots around the camp grounds, and they had plenty of ice which melts down into water. Plus, those campgrounds had lakes, but I didn't have to use the filter anyways since there was plenty of water.
I wouldn't personally map a route where I know I could be without a source of water or any sort, or some other liquids for more than 2 days during the ride.