Clean up unneeded flake-check duplication

The cachix action already only pushes from protected branches, based on
the presence of the auth token.

.github/workflows/build.yml

@@ -1,4 +1,5 @@
-name: check and push
+# CI that runs on pull requests and pushes to master.
+name: CI
 on:
   push:
     branches:
@@ -11,29 +12,14 @@ jobs:
   stack-test:
     uses: ./.github/workflows/stack-test.yml
 
-  flake-no-push:
-    name: flake check (no push)
-    if: github.event_name != 'push'
-    runs-on: ubuntu-latest
-    steps:
-      - uses: actions/checkout@v4
-      - uses: cachix/install-nix-action@v31
-      - uses: cachix/cachix-action@v15
-        with:
-          name: stackage-infrastructure
-      - run: nix build
-      - run: nix flake check
-
-  flake-push:
+  flake-check:
     name: flake check and push
     if: github.event_name == 'push'
     runs-on: ubuntu-latest
     steps:
-      - uses: actions/checkout@v4
+      - uses: actions/checkout@v6
       - uses: cachix/install-nix-action@v31
-      - uses: cachix/cachix-action@v15
-        with:
-          name: stackage-infrastructure
-          authToken: '${{ secrets.CACHIX_AUTH_TOKEN }}'
+      - uses: DeterminateSystems/magic-nix-cache-action@v13
+      - uses: cachix/cachix-action@v17
       - run: nix build
       - run: nix flake check