Check clang-tidy in tests.yaml (#3567)

Example success:
https://github.com/carbon-language/carbon-lang/actions/runs/7414437667/job/20175507192
Example failure:
https://github.com/carbon-language/carbon-lang/actions/runs/7414486486/job/20175656728

.github/workflows/tests.yaml

@@ -25,6 +25,10 @@ jobs:
         # https://github.com/actions/runner-images
         os: [ubuntu-22.04, macos-12]
         build_mode: [fastbuild, opt]
+        # The clang-tidy config doesn't work on macos (missing `truncate`).
+        include:
+          - os: 'ubuntu-22.04'
+            build_mode: 'clang-tidy'
     runs-on: ${{ matrix.os }}
 
     steps:
@@ -251,20 +255,22 @@ jobs:
           # Then use `target-determinator` as wrapped by our script.
           ./scripts/target_determinator.py $GIT_BASE_SHA >$TARGETS_FILE
 
+          # Bazel requires a test target to run the test command. There may be
+          # no targets or there may only be non-test targets that we want to
+          # build, so simply inject an explicit no-op test target.
+          echo "//scripts:no_op_test" >> $TARGETS_FILE
+
       # Build and run just the tests impacted by the PR or merge group.
       - name: Test (${{ matrix.build_mode }})
-        if: steps.filter.outputs.has_code == 'true'
+        if:
+          steps.filter.outputs.has_code == 'true' && matrix.build_mode !=
+          'clang-tidy'
         env:
           # 'libtool_check_unique failed to generate' workaround.
           # https://github.com/bazelbuild/bazel/issues/14113#issuecomment-999794586
           BAZEL_USE_CPP_ONLY_TOOLCHAIN: 1
           TARGETS_FILE: ${{ runner.temp }}/targets
         run: |
-          # Bazel requires a test target to run the test command. There may be
-          # no targets or there may only be non-test targets that we want to
-          # build, so simply inject an explicit no-op test target.
-          echo "//scripts:no_op_test" >> $TARGETS_FILE
-
           for i in {1..5}; do
             if (( $i == 4 )); then
               # Decrease the jobs sharply if we see repeated failures to try to
@@ -307,6 +313,20 @@ jobs:
           # Propagate the Bazel exit code.
           exit $bazel_exit
 
+      # Run in the clang-tidy config. This is done as part of tests so that we
+      # aren't duplicating bazel/llvm setup.
+      #
+      # The `-k` flag is used to print all clang-tidy errors.
+      - name: clang-tidy
+        if:
+          steps.filter.outputs.has_code == 'true' && matrix.os == 'ubuntu-22.04'
+          && matrix.build_mode == 'clang-tidy'
+        env:
+          TARGETS_FILE: ${{ runner.temp }}/targets
+        run: |
+          bazelisk build --config=clang-tidy -k \
+            --target_pattern_file=$TARGETS_FILE
+
       # See "Disk space before build".
       - name: Disk space after build
         if: steps.filter.outputs.has_code == 'true'