fix(ci): fix fern preview metadata and add continuous staging publish

[pdmack]

Summary

Fix two bugs in the Fern preview CI workflows, add offline link checking, and
extend the publish workflow to continuously deploy staging on docs commits to main.

Motivation / Context

The preview workflow was silently dropping PR metadata (PR_NUMBER empty,
HEAD_REF empty) because upload-artifact@v4 excludes hidden directories by
default. A second bug caused a corrupted GitHub API URL when posting the preview
comment. The publish workflow required a manual tag or dispatch to update the
docs site.

Fixes: N/A
Related: N/A

Type of Change

• Bug fix (non-breaking change that fixes an issue)
• New feature (non-breaking change that adds functionality)
• Build/CI/tooling

Component(s) Affected

• Other: Fern docs CI (.github/workflows/fern-docs-*.yml, publish-fern-docs.yml)

Implementation Notes

• .preview-metadata/ renamed to preview-metadata/ — upload-artifact@v4 sets
  include-hidden-files: false by default, silently excluding the directory from
  the artifact
• COMMENT_ID=$(... | tr -d '\r' | head -1) — gh api returns CRLF output;
  the trailing \r was included in the URL, causing
  parse "…/comments/{\r": invalid control character in URL
• Lychee runs --offline (file refs only) to avoid flaky external URL checks
• Publish concurrency group fern-publish with cancel-in-progress: true drops
  intermediate jobs on rapid merges to avoid consuming Fern API quota

Testing

CI-only change — no make qualify applicable. Workflows validated via
fern check (0 errors) and yamllint (0 errors).

Risk Assessment

• Low — Isolated change, well-tested, easy to revert

Rollout notes: N/A

Checklist

• Tests pass locally (make test with -race)
• Linter passes (make lint)
• I did not skip/disable tests to make CI green
• I added/updated tests for new functionality
• I updated docs if user-facing behavior changed
• Changes follow existing patterns in the codebase
• Commits are cryptographically signed (git commit -S)

[yuanchen8911]

/lgtm

Non-blocking note: the fern-publish concurrency group is shared by both main branch publishes and docs/v* tag publishes, so a rare overlap could cause one to cancel the other. This is low risk because fern generate --docs is idempotent and these events are infrequent. If you want to avoid branch-vs-tag cross-cancellation, consider scoping the group by ref type, e.g. fern-publish-${{ github.ref_type }}.