Dynamic vs static linking is mostly a red herring for desktop GUI application development unless you want to integrate into something like Linux distro package managers, as dynamic libraries on Mac and Windows can be self-contained within the application bundle/directory with no disadvantage beyond marginally longer startup time, and you can do similar things with Flatpak and friends on Linux.

The real difference is that Rust provides a package repository with a unified build system that's as simple to use as NPM or NuGet.

vcpkg which is similar exists today, but it didn't in 2015 when Discord started, still isn't anywhere near as comprehensive as package repositories for languages where package management is part of the standard toolchain, and the underlying build systems are far messier under the hood.

It can also be helpful in development to use libraries built from source as part of the application's build process, at least as an easily-accessible option, which wasn't common practice in most C/C++ ecosystems historically where different libraries used different build systems and if you wanted to integrate them into something like a Visual Studio solution for easy reference to source code during development and debugging you were often on your own.