Add backend framework

.github/workflows/backend.yml

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+name: Backend
+
+on:
+  push:
+  workflow_dispatch:
+
+env:
+  CARGO_TERM_COLOR: always
+
+jobs:
+  rust:
+    name: Rust
+    runs-on: ubuntu-latest
+    defaults:
+      run:
+        working-directory: ./backend
+    steps:
+      - uses: actions/checkout@v4
+      - name: Setup Rust
+        run: rustup update stable && rustup default stable
+      - name: Cargo cache
+        uses: actions/cache@v4
+        with:
+          path: |
+            ~/.cargo/.crates.toml
+            ~/.cargo/.crates2.json
+            ~/.cargo/bin/
+            ~/.cargo/registry/index/
+            ~/.cargo/registry/cache/
+            ~/.cargo/git/db/
+            target/
+          key: ${{ runner.os }}-cargo-${{ hashFiles('**/Cargo.lock') }}
+          restore-keys: ${{ runner.os }}-cargo-
+      - name: Install sqlx-cli
+        run: cargo install sqlx-cli --no-default-features --features sqlite
+      - name: Create database and run migrations
+        run: sqlx database setup
+      - name: Build
+        run: cargo build --verbose
+      - name: Check rustfmt
+        run: cargo fmt --all -- --check
+      - name: Check clippy
+        run: cargo clippy -- -D warnings
+      - name: Run tests
+        run: cargo test --verbose

backend/.env

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+DATABASE_URL=sqlite://db.sqlite

backend/.gitignore

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+/target
+db.sqlite*