ci: Extract docs release into reusable manual_release_docs.yaml workflow

[vdusek]

Follow-up to #857

Summary

• Rename _release_docs.yaml to manual_release_docs.yaml to match the naming convention of other reusable workflows (manual_version_docs.yaml, manual_release_stable.yaml).
• Add an optional ref input to workflow_dispatch so it can be triggered from the GitHub UI with a specific ref (falling back to the default branch).
• Replace the CHECKOUT_REF env var approach with a Determine checkout ref step, consistent with manual_version_docs.yaml.
• Update all references in manual_release_stable.yaml and on_master.yaml.

🤖 Generated with Claude Code

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 86.64%. Comparing base (0d26276) to head (eaa891d).
⚠️ Report is 2 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #858      +/-   ##
==========================================
- Coverage   86.67%   86.64%   -0.04%     
==========================================
  Files          48       48              
  Lines        2920     2920              
==========================================
- Hits         2531     2530       -1     
- Misses        389      390       +1     

Flag	Coverage Δ
e2e	37.87% <ø> (ø)
integration	59.28% <ø> (-0.04%)	⬇️
unit	74.69% <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.