docs(gates): widen relative-link checker to all docs, repair the rot it finds

TestDocsRelativeLinks walked only docs/developer; widening it to all of
docs/ immediately surfaced the same class of rot the gate was built
for, outside its old reach:

- docs/index.md was the old monolith's landing page: linked the deleted
  api-reference.md, 10 directory-style area links, and escaped the docs
  tree to README/AGENTS/.env/compose. Rewritten as a portal whose every
  link resolves, with one representative endpoint doc per API area and
  pointers to the new writing-ui-docs.md standard.
- directory-style links in user stubs (devices/, ../operations/)
- case-mismatched links (Development.md) in contributing.md
- monolith-era pointer (API_REFERENCE.md, TROUBLESHOOTING.md) and
  escaped AGENTS.md links in contributing/development.md
- docs/development/calibre-opf-implementation.md double-up escapes, a
  link to the removed repo-root plan file (absorbed here), and a
  source-code hyperlink the docs site can't serve (now inline code)
- operations/operations.md linked three never-written guide pages as
  aspirational links - they stay plain text until pages exist

HANDS-OFF (project owner, 2026-11-02): docs/user/filters/** and
docs/user/searching-and-filtering.md are exempt as link sources so no
future checker failure can force edits to the filter documentation.
Files linking INTO them remain checked.

docs/user/frontend-guide.md

@@ -13,4 +13,4 @@ This guide will cover:
 
 ---
 
-_In the meantime, check out our [Device Setup Guides](devices/)_
+_In the meantime, check out our [Device Setup Guides](devices/android-app.md) and [KOReader setup](devices/koreader-setup.md)_