ci: Rotate Docker cache keys every 4 weeks

This forces a periodic clean build to ensure we do not rely on stale
cache layers indefinitely.

.github/actions/run-in-docker-action/action.yml

@@ -6,8 +6,7 @@ inputs:
     required: true
   scope:
     description: 'A cached image scope'
-    required: false
-    default: ${{ runner.arch }}
+    required: true
   command:
     description: 'A command to run in a container'
     required: true

.github/workflows/ci.yml

@@ -48,6 +48,8 @@ jobs:
   docker_cache:
     name: "Build ${{ matrix.arch }} Docker image"
     runs-on: ${{ matrix.runner }}
+    outputs:
+      cache_scope: ${{ steps.cache_timestamp.outputs.period }}
 
     strategy:
       fail-fast: false
@@ -59,6 +61,10 @@ jobs:
             runner: ubuntu-24.04-arm
 
     steps:
+      - name: Get cache validity period
+        id: cache_timestamp
+        run: echo "period=$(($(date +%V) / 4))" >> "$GITHUB_OUTPUT"
+
       - name: Set up Docker Buildx
         uses: docker/setup-buildx-action@v3
         with:
@@ -70,8 +76,8 @@ jobs:
         uses: docker/build-push-action@v6
         with:
           file: ./ci/linux-debian.Dockerfile
-          cache-from: type=gha,scope=${{ runner.arch }}
-          cache-to: type=gha,scope=${{ runner.arch }},mode=min
+          cache-from: type=gha,scope=${{ runner.arch }}-${{ steps.cache_timestamp.outputs.period }}
+          cache-to: type=gha,scope=${{ runner.arch }}-${{ steps.cache_timestamp.outputs.period }},mode=min
 
   x86_64-debian:
     name: "x86_64: Linux (Debian stable)"
@@ -117,6 +123,7 @@ jobs:
         uses: ./.github/actions/run-in-docker-action
         with:
           dockerfile: ./ci/linux-debian.Dockerfile
+          scope: ${{ runner.arch }}-${{ needs.docker_cache.outputs.cache_scope }}
           command: ./ci/ci.sh
 
       - &PRINT_LOGS
@@ -636,6 +643,7 @@ jobs:
         uses: ./.github/actions/run-in-docker-action
         with:
           dockerfile: ./ci/linux-debian.Dockerfile
+          scope: ${{ runner.arch }}-${{ needs.docker_cache.outputs.cache_scope }}
           command: |
             g++ -Werror include/*.h
             clang -Werror -x c++-header include/*.h