[v3-1-test] Warn instead of failing on missing 3rd-party doc inventories (#63630) (#63646)

* Warn instead of failing on missing 3rd-party doc inventories

Third-party Sphinx intersphinx inventories (e.g., Pandas) are sometimes
temporarily unavailable. Previously, any download failure terminated the
entire doc build. Now missing 3rd-party inventories produce warnings and
fall back to cached versions when available. A marker file is written for
CI to detect missing inventories and send Slack notifications on canary
builds. Publishing workflows fail by default but can opt out.

- Add --fail-on-missing-third-party-inventories flag (default: off)
- Add --clean-inventory-cache flag (--clean-build no longer deletes cache)
- Cache inventories via stash action in CI and publish workflows
- Send Slack warning on canary builds when inventories are missing

* Add documentation for inventory cache handling options

Document the new --clean-inventory-cache, --fail-on-missing-third-party-inventories,
and --ignore-missing-inventories flags in the contributing docs, Breeze developer
tasks, and release management docs.

* Skip missing third-party inventories in intersphinx mapping

When a third-party inventory file doesn't exist in the cache,
skip it from the Sphinx intersphinx_mapping instead of referencing
a non-existent file. This prevents Sphinx build errors when
third-party inventory downloads fail.
(cherry picked from commit afda438816b8e8cd43ef105630c8f33da8ec98b5)