It does share dependencies, but in a different way than a regular package manager. You share runtimes and base apps: https://docs.flatpak.org/en/latest/dependencies.html

As other have pointed out, saying that "no dependencies are shared" is a very missinformed take, given that sharing dependencies as runtimes is an integral part of Flatpak's structure. But what makes it even funnier and more obvious that you don't know what your talking about, is that you than cite Nix as something you "vastly prefer" when Nix actually deals with dependencies in a very similar way to Flatpak. From the official site:

You can have multiple versions or variants of a package installed at the same time. This is especially important when different applications have dependencies on different versions of the same package — it prevents the “DLL hell”.

In both Flatpak and Nix, apps will only download a different version of a dependency when they need it. This ensure that, instead of breaking, the app will work the same on any system (be it an old stable Debian or a bleeding edge Arch system), without requiring devs to create monkey patches that they have to maintain as things evolve. It has the potential to immensely reduce the burden on app devs and maintainers, and make it a lot easier to make apps for Linux.