Limit docs publishing tests to canary run (apache#37196)

Docs publishing step takes a lot of disk space and time to complete, due
to size of the airflow-site repo. We should limit it to only run for
canary runs on self-hosted runners.

.github/workflows/ci.yml

@@ -767,25 +767,25 @@ jobs:
         run: >
           git clone https://github.com/apache/airflow-site.git ${GITHUB_WORKSPACE}/airflow-site &&
           echo "AIRFLOW_SITE_DIRECTORY=${GITHUB_WORKSPACE}/airflow-site" >> "$GITHUB_ENV"
-        if: needs.build-info.outputs.full-tests-needed == 'true'
+        if: needs.build-info.outputs.canary-run == 'true'
       - name: "Publish docs"
         run: >
           breeze release-management publish-docs
           --override-versioned --run-in-parallel
           ${{ needs.build-info.outputs.docs-list-as-string }}
-        if: needs.build-info.outputs.full-tests-needed == 'true'
+        if: needs.build-info.outputs.canary-run == 'true'
       - name: "Generate back references for providers"
         run: breeze release-management add-back-references all-providers
-        if: needs.build-info.outputs.full-tests-needed == 'true'
+        if: needs.build-info.outputs.canary-run == 'true'
       - name: "Generate back references for apache-airflow"
         run: breeze release-management add-back-references apache-airflow
-        if: needs.build-info.outputs.full-tests-needed == 'true'
+        if: needs.build-info.outputs.canary-run == 'true'
       - name: "Generate back references for docker-stack"
         run: breeze release-management add-back-references docker-stack
-        if: needs.build-info.outputs.full-tests-needed == 'true'
+        if: needs.build-info.outputs.canary-run == 'true'
       - name: "Generate back references for helm-chart"
         run: breeze release-management add-back-references helm-chart
-        if: needs.build-info.outputs.full-tests-needed == 'true'
+        if: needs.build-info.outputs.canary-run == 'true'
       - name: Configure AWS credentials
         uses: aws-actions/configure-aws-credentials@010d0da01d0b5a38af31e9c3470dbfdabdecca3a  # v4.0.1
         if: needs.build-info.outputs.canary-run == 'true' && needs.build-info.outputs.default-branch == 'main'

dev/breeze/doc/ci/05_workflows.md

@@ -237,7 +237,7 @@ code.
 | Upgrade checks                  | Performs checks if there are some pending upgrades       |          | Yes      | Yes        | Yes              |
 | Static checks                   | Performs full static checks                              | Yes (6)  | Yes      | Yes        | Yes (7)          |
 | Basic static checks             | Performs basic static checks (no image)                  | Yes (6)  |          |            |                  |
-| Build docs                      | Builds and tests publishing of the documentation         | Yes      | Yes      | Yes        | Yes              |
+| Build docs                      | Builds and tests publishing of the documentation         | Yes      | Yes (11) | Yes        | Yes              |
 | Spellcheck docs                 | Spellcheck docs                                          | Yes      | Yes      | Yes        | Yes              |
 | Tests wheel provider packages   | Tests if provider packages can be built and released     | Yes      | Yes      | Yes        |                  |
 | Tests Airflow compatibility     | Compatibility of provider packages with older Airflow    | Yes      | Yes      | Yes        |                  |
@@ -293,6 +293,9 @@ via `skip-provider-tests` selective check output.
 `(10)` Only run the builds in case PR is run by a committer from
 "apache" repository and in scheduled build.
 
+`(11)` Docs publishing is only done in Canary run, to handle the case where
+cloning whole airflow site on Public Runner cannot complete due to the size of the repository.
+
 ## CodeQL scan
 
 The [CodeQL](https://securitylab.github.com/tools/codeql) security scan