docs(ui): cookie-rendered sidebar state, data-collapsed CSS, working overview links + link-checker gate

Three problems, one root cause each:

1. Sidebar jump: the server rendered its own default (current section
   open, rest collapsed) and restoreDocsNav corrected it after paint —
   open-then-close. Fix: persistence moved server-side. toggleCollapsible
   now writes a docs_nav cookie (strictly-necessary UI state, no
   identifiers, SameSite=Lax); ApplyNavOverrides merges it into the nav
   before render, so first paint IS the visitor's state. The post-paint
   restore is deleted.

2. Arrows out of sync / double-click: two visibility mechanisms
   disagreed. There was NO data-collapsed CSS at all — collapsed sections
   were only ever hidden by JS after paint, and the arrow rotation came
   from a different (server) state. Now: style.css hides on
   [data-collapsed=true] (single source of truth, server-rendered),
   applyCollapsed sets only the attribute, arrows rotate from the same
   merged value. Live check: 37/37 collapsibles arrow-consistent.

3. api-reference.md links: all 20+ quick links were directory-style
   (authentication/ etc.) that 404 on the docs site, plus stale targets
   (books/, ../collections-api.md, websocket 'coming soon'). Rewritten to
   real per-file links — all 9 unique targets return 200 live. Same rot
   fixed in admin/hash-conflicts.md, development.md, android-app.md,
   create_media_item.md, koreader-protocol.md; docs/index.md redirected
   from the deleted collections-api monolith (stale 530-line duplicate of
   the gated api/collections docs — deleted, per the WO2 doctrine).

New gate: TestDocsRelativeLinks walks docs/developer/** and fails make
test on any relative link that is directory-style or unresolvable —
overview links can never silently rot again.

web/static/input.css

@@ -2105,3 +2105,11 @@
     font-size: 0.78rem;
     color: var(--text-secondary);
   }
+
+/* Docs sidebar: the data-collapsed attribute is the single source of truth
+   for section/group visibility. The server renders it (navigation defaults
+   + docs_nav cookie overrides); toggleCollapsible updates it in place. */
+.nav-items[data-collapsed="true"],
+.nav-group-items[data-collapsed="true"] {
+  display: none;
+}