Add rust lint CI job. (#9)

Additionally fix the many lint errors that are occurring. (or disable them).

Reviewed-on: #9
Co-authored-by: Drew Galbraith <drew@tiramisu.one>
Co-committed-by: Drew Galbraith <drew@tiramisu.one>

.forgejo/workflows/ci.yml

@@ -0,0 +1,42 @@
+name: Check
+
+on:
+  push:
+    branches: [main]
+  pull_request:
+    branches: [main]
+
+env:
+  # Should speed up builds.
+  CARGO_INCREMENTAL: 0
+  # Should reduce the size of ./target to improve cache load/store.
+  CARGO_PROFILE_TEST_DEBUG: 0
+
+jobs:
+  check:
+    name: Check Rust
+    runs-on: docker
+
+    steps:
+      - name: Checkout Repo
+        uses: actions/checkout@v4
+
+      - name: Install Rust
+        uses: https://codeberg.org/wackbyte/rust-toolchain@trunk
+        with:
+          toolchain: nightly-2025-10-02
+          components: rustfmt, clippy, rust-src
+      - name: Cache
+        uses: https://github.com/Swatinem/rust-cache@v2
+        with:
+          # Don't cache ~/.cargo/bin since we restore the cache after we install things there
+          cache-bin: "false"
+          workspaces: "backend"
+      - name: "Check Format"
+        run: cargo fmt --check
+        working-directory: rust
+      - name: "Lint"
+        run: |
+          rustup component add clippy
+          cargo clippy --locked -- -D warnings
+        working-directory: rust