Add formatter GH action

.github/workflows/julia_formatter.yml

@@ -0,0 +1,43 @@
+name: JuliaFormatter
+
+on:
+  push:
+    branches:
+      - main
+    tags: '*'
+  pull_request:
+  merge_group:
+
+jobs:
+  format:
+    runs-on: ubuntu-latest
+    timeout-minutes: 30
+    steps:
+    - name: Cancel Previous Runs
+      uses: styfle/[email protected]
+      with:
+        access_token: ${{ github.token }}
+
+    - uses: actions/[email protected]
+
+    - uses: dorny/[email protected]
+      id: filter
+      with:
+        filters: |
+          julia_file_change:
+            - added|modified: '**.jl'
+
+    - uses: julia-actions/setup-julia@latest
+      if: steps.filter.outputs.julia_file_change == 'true'
+      with:
+        version: 1.10
+
+    - name: Apply JuliaFormatter
+      if: steps.filter.outputs.julia_file_change == 'true'
+      run: |
+        julia --project=.dev .dev/climaformat.jl .
+
+    - name: Check formatting diff
+      if: steps.filter.outputs.julia_file_change == 'true'
+      run: |
+        git diff --color=always --exit-code