I don’t any experience with Nix - but how does it handle software which runs its own updating processes outside the package manager? Specifically thinking about software like Discord, Slack, Docker Desktop, Jetbrains Toolbox, etc. Is the Nix-ism to just reject using such software?
Jetbrains Toolbox is in a sort of different category with tools like Rustup, since it's a package manager of its own. If you manage your IDEs with Toolbox, then your IDE versions are "outside Nix" and not managed by Nix. It's just packaged into its own pretend FHS environment and then doesn't know anything about it being on Nix. That said, updates of Toolbox itself will need to happen through your package manager.
As a last comment, why run Docker Desktop on Linux at all? Like I understand on Windows and Mac - docker is inherently tied to Linux so the Windows/Mac apps abstract away the fact that it's running a VM and doing a bunch of port mapping and filesystem mounting under the hood so you can pretend it's not running on a VM, but on Linux I've always just installed docker straight onto the host.