Create simple CI workflow

.gitea/workflows/build-test.yml

@@ -0,0 +1,52 @@
+name: Build & Test
+
+on:
+  push:
+    branches:
+      - main
+  pull_request:
+    branches:
+      - '*'
+
+jobs:
+  build-backend:
+    steps:
+      - name: Checkout code
+        uses: actions/checkout@v4
+
+      - name: Set up .NET
+        uses: actions/setup-dotnet@v5
+        with:
+          dotnet-version: '10.0.x'
+
+      - name: Restore .NET Tools
+        run: dotnet tool restore
+
+      - name: Check formatting
+        run: dotnet csharpier format .
+
+      - name: Build
+        run: dotnet build
+
+      - name: Test
+        run: dotnet test
+
+  build-frontend:
+    defaults:
+      run:
+        working-directory: ./src/mission-control-client
+    steps:
+      - name: Checkout code
+        uses: actions/checkout@v4
+
+      - name: Install dependencies
+        run: npm ci
+
+      - name: Check formatting
+        run: npm run format:check
+
+      - name: Build
+        run: npm run build
+
+      - name: Test
+        run: npm test