Refactor Nix flake to use crane (#7763)

This resolves a build issue with nci/dream2nix and git dependencies.
We can keep most of the helix-specific parts of the flake, we just need
to switch from configuring nci to calling craneLib functions.

We also switch to flake-utils from flake-parts:

* Using rust-overlay with flake-parts directly is unergonomic
  (see https://github.com/hercules-ci/flake-parts/discussions/83).
* Removing flake-parts reduces the overall dependencies: rust-overlay
  already depends on flake-utils.

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