ci: fix CI pipeline and improve test reliability

- Convert repository name to lowercase for Docker image tags (GHCR requirement)
- Disable Redis caching during integration tests to avoid connection errors
- Mock Firebase initialization in tests to eliminate missing service account warning
- Increase JWT secret length to meet security requirements (256 bits)
- Make BackendApplicationTests use embedded MongoDB via BaseIntegrationTest

Author: harman-04

.github/workflows/ci.yml

@@ -8,8 +8,6 @@ on:
 
 env:
   REGISTRY: ghcr.io
-  IMAGE_NAME_BACKEND: ${{ github.repository }}/backend
-  IMAGE_NAME_FRONTEND: ${{ github.repository }}/frontend
 
 jobs:
   test-backend:
@@ -66,18 +64,27 @@ jobs:
       packages: write
     steps:
       - uses: actions/checkout@v4
+
+      - name: Set lowercase image names
+        run: |
+          REPO_LC=$(echo "${{ github.repository }}" | tr '[:upper:]' '[:lower:]')
+          echo "IMAGE_NAME_BACKEND=${REPO_LC}/backend" >> $GITHUB_ENV
+          echo "IMAGE_NAME_FRONTEND=${REPO_LC}/frontend" >> $GITHUB_ENV
+
       - name: Log in to GitHub Container Registry
         uses: docker/login-action@v3
         with:
           registry: ghcr.io
           username: ${{ github.actor }}
           password: ${{ secrets.GITHUB_TOKEN }}
+
       - name: Build and push backend
         uses: docker/build-push-action@v5
         with:
           context: ./backend/backend
           push: true
           tags: ${{ env.REGISTRY }}/${{ env.IMAGE_NAME_BACKEND }}:latest, ${{ env.REGISTRY }}/${{ env.IMAGE_NAME_BACKEND }}:${{ github.sha }}
+
       - name: Build and push frontend
         uses: docker/build-push-action@v5
         with: