S23.17: Fix Core/Platforms/Roles doorways vanishing from the narrow nav drawer #629

Problem

On narrow viewports the nav collapses from the horizontal tabs into the hamburger drawer, which is a drill-down (one panel per level, back-arrow to ascend). On the API reference landing — and the Doxygen index pages (Headers / Data structures / Functions / Macros) — the drawer opens inside a redundant nested section, so its siblings Core / Platforms / Roles sit one level up and are hidden behind the back arrow. The wide sidebar is fine (navigation.sections flattens above 1220px); only the drawer is affected.

Root cause

The "API reference" tab wraps its Doxygen indexes in a nested section also named "API reference", pushing the tab's own landing page a level below the doorways. Confirmed: on /api-reference/ the active drawer panel is the nested section; on /core/ it's the tab, where the doorways show.

Fix

• Promote api-reference/index.md to the tab's own first child, so navigation.indexes makes it the tab link and the landing opens the drawer at tab level.
• Relabel the Doxygen-index group from "API reference" to "Headers and Symbols" so it's a real peer of Core / Platforms / Roles, not a same-named wrapper.

Result: the drawer opens at the tab, with all four peers (Headers and Symbols, Core, Platforms, Roles) visible. Raw Doxygen index pages still drill one level in, which is normal mobile behaviour.

Notes

• Depends on docs: S23.16 Core page, architecture overview, and PlusTcpResolver accuracy fix #628 (S23.16), which adds the Core doorway; this branches off main after that merges so the fix slots into the merged structure.
• Fix is already prototyped and verified against the local serve (active drawer panel drops from the nested section to the tab).

Parent epic: #246