ci: clean up the flake-lock update action

Now that only the internal flake has actual inputs, we only need one of
these actions running instead of two.

.github/workflows/update-flake.yml

@@ -1,4 +1,4 @@
-name: Update flake dependencies
+name: Update internal flake dependencies
 
 on:
   workflow_dispatch: # for allowing manual triggers of the workflow
@@ -27,7 +27,8 @@ jobs:
       with:
         token: ${{ secrets.PAT_FLAKE_UPDATE }}
         branch: "automation/flake-update"
-        pr-title: "Update flake.lock"
+        pr-title: "Update internal flake.lock"
+        path-to-flake-dir: ./test
         pr-labels: |
           automated
           dependencies

.github/workflows/update-test-flake.yml

@@ -1,40 +0,0 @@
-name: Update internal flake dependencies
-
-on:
-  workflow_dispatch: # for allowing manual triggers of the workflow
-  schedule:
-    - cron: '37 16 9,24 * *'
-
-permissions:
-  contents: read
-
-jobs:
-  update-and-push-deps:
-    runs-on: ubuntu-latest
-    steps:
-    - uses: actions/checkout@v4
-    - uses: cachix/install-nix-action@V27
-      with:
-        extra_nix_config: |
-          access-tokens = github.com=${{ secrets.GITHUB_TOKEN }}
-    - uses: cachix/cachix-action@v15
-      with:
-        name: crane
-        authToken: '${{ secrets.CACHIX_AUTH_TOKEN }}'
-    - name: Update flake.lock
-      id: flakeupdate
-      uses: DeterminateSystems/update-flake-lock@v23
-      with:
-        token: ${{ secrets.PAT_FLAKE_UPDATE }}
-        branch: "automation/flake-update-internal"
-        path-to-flake-dir: ./test
-        pr-title: "Update internal flake.lock"
-        pr-labels: |
-          automated
-          dependencies
-          flake update
-    - name: Enable Pull Request Automerge
-      run: gh pr merge --squash --delete-branch --auto ${{ steps.flakeupdate.outputs.pull-request-number }}
-      env:
-        GH_TOKEN: ${{ secrets.PAT_FLAKE_UPDATE }}
-