@Thorfinn Those are all good points. If it were up to me, drinking straight from the freshwater block would be something I'd add, but only giving small amounts of hydration per drink, since you're effectively cupping your hands and drinking like that. Having skins/clay jugs and eventually bottles would help, allowing the player to carry water supplies wherever they go.
Yeah, the current inventory is already pretty small honestly, I tend to use mods that enhance the backpack capacities. I think having them be simple inventory items would work, although a mod for something like a camelbak that you wear that holds a lot of water and you could drink from would be cool.
For islands, I think coconuts and rain collectors crafted from logs and plant fibres would help a lot, maybe any other plants that could give water as well. Once you've got materials, making a distillery could allow you to desalinate the water from the ocean, and maybe give a very small amount of salt as well.
For deserts, I think some kind of moisture collector might be interesting. I don't really know too much about it or even if it's doable with only primitive tech, I just remember seeing some in the Mad Max game made out of tarp and buckets and I thought they were a really cool idea. Maybe hides and buckets in this case, or some kind of large windmill looking structure that funnels water into a metal tank? Other than that, I think the main issue with deserts would always be the lack of food and water, or at least those resources in large amounts.