feat: 머지하기 전, back build test

#139

.github/workflows/back-build-test.yml

@@ -0,0 +1,31 @@
+name: back build test
+
+on:
+  pull_request:
+    branches: ["main"]
+  workflow_dispatch:
+
+jobs:
+  back_build_test:
+    runs-on: ubuntu-24.04
+    timeout-minutes: 10
+
+    permissions:
+      id-token: write
+      contents: read
+
+    steps:
+      - uses: actions/checkout@v4
+      - name: Set up JDK 17
+        uses: actions/setup-java@v4
+        with:
+          java-version: "17"
+          distribution: "temurin"
+
+      - name: Setup Gradle
+        uses: gradle/actions/setup-gradle@dbbdc275be76ac10734476cc723d82dfe7ec6eda # v3.4.2
+
+      - name: Build with Gradle Wrapper
+        run: |
+          cd backend
+          ./gradlew build