Add clang-tidy configuration and CI job

.clang-tidy

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+---
+Checks: >
+  -*,
+  clang-analyzer-*,
+  clang-diagnostic-*,
+  bugprone-*,
+  performance-*
+WarningsAsErrors: '*'
+# Only analyze headers from this repository; ignore external headers
+HeaderFilterRegex: '^(include/|test/(?!third_party/))'
+FormatStyle: file
+...

.github/workflows/clang-tidy-review.yml

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+name: clang-tidy-review
+
+on: [pull_request]
+
+jobs:
+  build:
+    runs-on: ubuntu-latest
+
+    steps:
+    - uses: actions/checkout@v4
+
+    # Optionally generate compile_commands.json
+    - uses: ZedThree/clang-tidy-review@v0.21.0
+      id: review
+      with:
+        cmake_command: cmake -S . -B build -DCMAKE_EXPORT_COMPILE_COMMANDS=ON
+        build_dir: build
+
+    # Uploads an artefact containing clang_fixes.json
+    - uses: ZedThree/clang-tidy-review/upload@v0.21.0
+      id: upload-review
+
+    # If there are any comments, fail the check
+    - if: steps.review.outputs.total_comments > 0
+      run: exit 1