nix: don't drag rust toolchain into system closures

flake.nix

@@ -3,17 +3,12 @@
 
   inputs = {
     nixpkgs.url = "github:NixOS/nixpkgs/nixos-unstable";
-    rust-overlay = {
-      url = "github:oxalica/rust-overlay";
-      inputs.nixpkgs.follows = "nixpkgs";
-    };
   };
 
   outputs =
     {
       self,
       nixpkgs,
-      rust-overlay,
     }:
     let
       systems = [
@@ -26,7 +21,6 @@
         system:
         import nixpkgs {
           inherit system;
-          overlays = [ rust-overlay.overlays.default ];
         };
 
       perSystem =
@@ -34,13 +28,6 @@
         let
           pkgs = pkgsFor system;
 
-          rustToolchain = pkgs.rust-bin.fromRustupToolchainFile ./rust-toolchain.toml;
-
-          rustPlatform = pkgs.makeRustPlatform {
-            cargo = rustToolchain;
-            rustc = rustToolchain;
-          };
-
           # Native libs the audio crates link against.
           nativeAudioBuildInputs = with pkgs; [
             pipewire
@@ -64,8 +51,11 @@
               name = "headroom-dev";
 
               nativeBuildInputs = nativeBuildTools ++ [
-                rustToolchain
+                pkgs.cargo
+                pkgs.clippy
                 pkgs.rust-analyzer
+                pkgs.rustc
+                pkgs.rustfmt
               ];
 
               buildInputs =
@@ -89,7 +79,7 @@
           );
 
           # `nix build` — the final packaged daemon + CLI.
-          headroom = rustPlatform.buildRustPackage (
+          headroom = pkgs.rustPlatform.buildRustPackage (
             {
               pname = "headroom";
               # Pull from the workspace Cargo.toml — the per-crate