Generate job annotations without GHA REST API

The separate annotate workflow was added to work around permission
issues in forked repositories. This is not needed when not using the GHA
REST API.

Adding annotations via the API was not working correctly
anyway, since it added a check for a commit, but one commit can have
multiple runs associated with it, and the check sometimes did not show
up in the main run.

.github/actions/process-test-results/action.yml

@@ -28,18 +28,6 @@ runs:
         testing/trino-product-tests/target/*
         logs/*
       retention-days: 5
-  - name: Upload test report
-    uses: actions/upload-artifact@v4
-    # Always upload the test report for the annotate.yml workflow,
-    # but only the single XML file to keep the artifact small
-    with:
-      # Name prefix is checked in the `Annotate checks` workflow
-      name: test report ${{ inputs.artifact-name }}
-      if-no-files-found: 'ignore'
-      path: |
-        **/surefire-reports/TEST-*.xml
-        testing/trino-product-tests/target/reports/**/testng-results.xml
-      retention-days: 5
   - name: Upload heap dump
     uses: actions/upload-artifact@v4
     if: format('{0}', inputs.upload-heap-dump) == 'true'
@@ -49,3 +37,20 @@ runs:
       path: |
         **/*.hprof
       retention-days: 14
+  - name: Process unit and integration test reports
+    uses: trinodb/github-actions/action-surefire-report@b63800bedfbc7ab1ff2e5fe7eaecf5ab82ce6a70
+    if: format('{0}', inputs.has-failed-tests) == 'true'
+    with:
+      # this workflow should never fail, as it is not a quality gateway
+      fail_if_no_tests: false
+      # don't create or update checks, only annotate current job
+      skip_publishing: true
+  - name: Process Product Test reports
+    uses: starburstdata/action-testng-report@f245422953fb97ec5075d07782a1b596124b7cc4
+    if: format('{0}', inputs.has-failed-tests) == 'true'
+    with:
+      # this workflow should never fail, as it is not a quality gateway
+      fail_if_empty: false
+      github_token: ${{ github.token }}
+      # don't create or update checks, only annotate current job
+      skip_publishing: true