ci: add Forgejo action to build and push Docker images to registry

.forgejo/workflows/docker-build.yml

@@ -0,0 +1,45 @@
+name: Build and push Docker images
+
+on:
+  push:
+    branches:
+      - main
+      - master
+  workflow_dispatch:
+
+jobs:
+  build:
+    runs-on: ubuntu-latest
+    strategy:
+      fail-fast: false
+      matrix:
+        include:
+          - service: claude
+            context: ./claude
+          - service: proxy
+            context: ./proxy
+
+    steps:
+      - name: Checkout
+        uses: actions/checkout@v4
+
+      - name: Set up Docker Buildx
+        uses: docker/setup-buildx-action@v3
+
+      - name: Log in to ${{ vars.REGISTRY_URL }}
+        uses: docker/login-action@v3
+        with:
+          registry: ${{ vars.REGISTRY_URL }}
+          username: ${{ vars.REGISTRY_USER }}
+          password: ${{ secrets.REGISTRY_PASSWORD }}
+
+      - name: Build and push ${{ matrix.service }}
+        uses: docker/build-push-action@v5
+        with:
+          context: ${{ matrix.context }}
+          push: true
+          tags: |
+            ${{ vars.REGISTRY_URL }}/${{ vars.REGISTRY_USER }}/${{ matrix.service }}:latest
+            ${{ vars.REGISTRY_URL }}/${{ vars.REGISTRY_USER }}/${{ matrix.service }}:${{ github.sha }}
+          cache-from: type=registry,ref=${{ vars.REGISTRY_URL }}/${{ vars.REGISTRY_USER }}/${{ matrix.service }}:cache
+          cache-to: type=registry,ref=${{ vars.REGISTRY_URL }}/${{ vars.REGISTRY_USER }}/${{ matrix.service }}:cache,mode=max