ci(treewide): add deadnix

deadnix is a package to find unused nix code, we can add it to enforce
that we don't leave let bindings/inputs/etc. around when they are not
needed

.tangled/workflows/deadnix.yml

···
+# SPDX-FileCopyrightText: 2025 FreshlyBakedCake
+#
+# SPDX-License-Identifier: MIT
+
+when:
+  - event: ["push", "pull_request"]
+    branch: ["main"]
+
+engine: nixery
+
+dependencies:
+  nixpkgs:
+    - ansifilter
+    - deadnix
+
+steps:
+  - name: Check for unused nix bindings
+    command: |
+      set -eo pipefail
+
+      deadnix --exclude **/npins --no-underscore --fail | ansifilter

packetmix/nilla.nix

···
               config.inputs.nilla-home.result.packages.nilla-home.result.${system}
               config.inputs.nilla-nixos.result.packages.nilla-nixos.result.${system}
               config.inputs.nixos-unstable.result.${system}.quickshell
+              config.inputs.nixpkgs.result.${system}.deadnix
               config.packages.nilla-fmt.result.${system}
               config.packages.treefmt.result.${system}
               (config.inputs.npins.result { inherit pkgs system; })