I think it’s more accurate to say they will install different libraries for every package unless there’s a matching library already installed. I don’t think this is just semantics because, as you say, the former is what traditional distro managers do, whereas the latter is what Snap does. The Snap-based system will end up taking more space, with more different versions of the same library installed, than a traditional system over time. For that, you trade (arguably) fewer dependency-related issues, and more ability to concurrently run software with conflicting library versions. Regardless of the benefits, per the question OP posed, a Snap (or Flatpack) based distro will end up taking up more space.

I haven’t run Gentoo in decade(s, almost), but IIRC you could configure it to build mostly statically-linked packages, which would pretty much net you OP’s hypothetical system. That would be even larger than a Snap-based system.