ci add github actions workflow for rust workspace checks

Run cargo check for the backend workspace with required Postgres build dependencies on push/pull_request.

Made-with: Cursor

.github/workflows/ci.yml

@@ -0,0 +1,31 @@
+name: Rust Backend CI
+
+on:
+  push:
+    branches:
+      - master
+      - main
+  pull_request:
+
+jobs:
+  check:
+    runs-on: ubuntu-latest
+    timeout-minutes: 30
+
+    steps:
+      - name: Checkout
+        uses: actions/checkout@v4
+
+      - name: Install system dependencies
+        run: |
+          sudo apt-get update
+          sudo apt-get install -y libpq-dev pkg-config clang
+
+      - name: Setup Rust toolchain
+        uses: dtolnay/rust-toolchain@stable
+
+      - name: Cache cargo registry and target
+        uses: Swatinem/rust-cache@v2
+
+      - name: Cargo check workspace
+        run: cargo check --workspace --all-targets