chore: Add GitHub Actions workflow to build and publish Docker image

.github/workflows/build-api.yml

@@ -0,0 +1,32 @@
+name: Build and Publish Docker Image
+
+on:
+  push:
+    branches:
+      - main
+
+jobs:
+  build-mongo-api:
+    runs-on: ubuntu-latest
+
+    steps:
+    - name: Checkout code
+      uses: actions/checkout@v2
+
+    - name: Set up Docker Buildx
+      uses: docker/setup-buildx-action@v1
+
+    - name: Login to GitHub Container Registry
+      uses: docker/login-action@v2
+      with:
+        registry: ghcr.io
+        username: nmcc1212
+        password: ${{ secrets.GHCR_PAT }}
+
+    - name: Build and push Docker image
+      uses: docker/build-push-action@v2
+      with:
+        context: .
+        file: newAPI/Dockerfile
+        push: true
+        tags: ghcr.io/nmcc1212/cacher:latest