build(deps): bump cachix/install-nix-action from 20 to 22

Bumps [cachix/install-nix-action](https://github.com/cachix/install-nix-action) from 20 to 22.
- [Release notes](https://github.com/cachix/install-nix-action/releases)
- [Commits](cachix/install-nix-action@v20...v22)

---
updated-dependencies:
- dependency-name: cachix/install-nix-action
  dependency-type: direct:production
  update-type: version-update:semver-major
...

Signed-off-by: dependabot[bot] <[email protected]>

Author: dependabot[bot]

.github/workflows/developer_productivity.yml

@@ -32,7 +32,7 @@ jobs:
       - name: Checkout sources
         uses: actions/checkout@v3
       - uses: Swatinem/rust-cache@v2
-      - uses: cachix/install-nix-action@v20
+      - uses: cachix/install-nix-action@v22
         with:
           # This channel is only required to invoke "nix-shell".
           # Everything inside that nix-shell will use a pinned version of nixpkgs.