ci: Trigger doc release on stable release

[vdusek]

Summary

• The stable release pipeline was missing a doc release step, so the changelog on the website was not updated after a stable release
• Added a doc_release job to manual_release_stable.yaml (same pattern as doc_release_post_publish in on_master.yaml)
• The job runs after changelog_update and pypi_publish, using the changelog commit ref to include the updated changelog
• Includes explicit permissions (contents: write, pages: write, id-token: write) since the workflow has top-level permissions: contents: read

Test plan

• Verify the workflow YAML is valid
• Trigger a stable release and confirm doc release runs

🤖 Generated with Claude Code

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 76.02%. Comparing base (9ca9d44) to head (550fa2a).
⚠️ Report is 6 commits behind head on master.

Additional details and impacted files

@@           Coverage Diff           @@
##           master     #625   +/-   ##
=======================================
  Coverage   76.02%   76.02%           
=======================================
  Files          42       42           
  Lines        2482     2482           
=======================================
  Hits         1887     1887           
  Misses        595      595           

Flag	Coverage Δ
integration	68.77% <ø> (ø)
unit	65.31% <ø> (ø)

Flags with carried forward coverage won't be shown. Click here to find out more.

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.
• 📦 JS Bundle Analysis: Save yourself from yourself by tracking and limiting bundle sizes in JS merges.

[vdusek]

@janbuchar Could you please confirm that this is the correct approach?

[janbuchar]

LGTM, let's test it out