Introduce a cargo clippy run (#2025)

This might help catch stylistic problems in our Rust code.

Related to #2587.

.github/workflows/build.yml

@@ -11,38 +11,6 @@ env:
   CARGO_TERM_COLOR: always
 
 jobs:
-  format:
-    runs-on: ubuntu-latest
-    env:
-      NIGHTLY_VERSION: nightly-2025-09-01
-    steps:
-      - name: Checkout
-        uses: actions/checkout@v5
-
-      - name: Install formatting dependencies
-        run: |
-          sudo apt update
-          sudo apt install gettext yapf3
-
-      - name: Install pinned nightly for rustfmt
-        run: |
-          rustup toolchain install --profile minimal "$NIGHTLY_VERSION"
-          rustup component add rustfmt --toolchain "$NIGHTLY_VERSION"
-
-      - name: Check formatting
-        uses: dprint/check@v2.3
-
-  typos:
-    runs-on: ubuntu-latest
-    steps:
-      - name: Checkout
-        uses: actions/checkout@v5
-
-      - name: Check for typos
-        uses: crate-ci/typos@v1.35.7
-        with:
-          config: ./.github/typos.toml
-
   cargo:
     strategy:
       matrix:

.github/workflows/lint.yml

@@ -0,0 +1,55 @@
+name: Lint
+
+on:
+  pull_request:
+  push:
+    branches:
+      - main
+
+env:
+  CARGO_TERM_COLOR: always
+
+jobs:
+  clippy:
+    runs-on: ubuntu-latest
+    steps:
+      - name: Checkout
+        uses: actions/checkout@v5
+
+      - name: Setup Rust cache
+        uses: ./.github/workflows/setup-rust-cache
+
+      - name: Clippy
+        run: cargo clippy -- -Dwarnings
+
+  format:
+    runs-on: ubuntu-latest
+    env:
+      NIGHTLY_VERSION: nightly-2025-09-01
+    steps:
+      - name: Checkout
+        uses: actions/checkout@v5
+
+      - name: Install formatting dependencies
+        run: |
+          sudo apt update
+          sudo apt install gettext yapf3
+
+      - name: Install pinned nightly for rustfmt
+        run: |
+          rustup toolchain install --profile minimal "$NIGHTLY_VERSION"
+          rustup component add rustfmt --toolchain "$NIGHTLY_VERSION"
+
+      - name: Check formatting
+        uses: dprint/check@v2.3
+
+  typos:
+    runs-on: ubuntu-latest
+    steps:
+      - name: Checkout
+        uses: actions/checkout@v5
+
+      - name: Check for typos
+        uses: crate-ci/typos@v1.35.7
+        with:
+          config: ./.github/typos.toml