add docker-c workflow

.github/workflows/docker-c.yml

@@ -0,0 +1,39 @@
+name: Rebuild C Docker image
+
+# Only run manually for now
+on:
+  workflow_dispatch:
+  push:
+
+env:
+  REGISTRY: ghcr.io
+  IMAGE_NAME: ${{ github.repository }}-c
+
+jobs:
+  build-and-push-image:
+    runs-on: ubuntu-latest
+
+    # We need write access to packages
+    permissions:
+      contents: read
+      packages: write
+      attestations: write
+      id-token: write
+
+    steps:
+      - uses: actions/checkout@v4
+
+      - name: Log in to the Container registry
+        uses: docker/login-action@9780b0c442fbb1117ed29e0efdff1e18412f7567
+        with:
+          registry: ${{ env.REGISTRY }}
+          username: ${{ github.actor }}
+          password: ${{ secrets.GITHUB_TOKEN }}
+
+      - name: Build and push Docker image
+        id: push
+        uses: docker/build-push-action@4f58ea79222b3b9dc2c8bbdd6debcef730109a75
+        with:
+          context: .docker/c/
+          push: true
+          tags: latest