How does it stack up against traditional package management and others like AUR and Nix?
Man this Missinformationen is hard to squash. Yes Flatpaks absolutely share libraries. These are called runtimes and are shared between all the Flatpak apps that use the same version of it. You will only get more than one version of a given runtime if some apps need this other version. For most runtimes that I know of, most only have 2 currently maintained versions, so I almost never get more than that on my system (and when I do, app devs tend to update their apps shortly after so that they’re using a maintained runtime). For example on my system where I mostly use GTK apps, I only have two versions of the Gnome runtime (44 and 45). And even when you have more than one version of a runtime, they get deduplicated, so even runtimes share parts between them.
If you’re interested here is an article about it.