feat(theming): dropdown sections and added links in the public header

Phase 10 of docs/website/THEMING_AND_NAV.md, asked for before the edge -> main
cutover. An admin can now create dropdown sections in the public header, organise
the coded entries into them, and add links of their own.

This deliberately amends §7, which said the override layer "cannot introduce a
`to` that is not already in the hardcoded NAV array". That stays true of every
CODED entry; an admin may now also add a link, restricted to a same-origin path —
no scheme, no protocol-relative //host. A link carries no gate of its own and
needs none: the page behind it enforces its own access, so an added link
advertises a route and never grants one.

The invariant is kept structurally rather than by vigilance. Coded entries live
in an `items` map whose keys must be routes the base array declares, so that map
cannot invent a route; everything that CAN name an arbitrary path lives in
`links`, which is the one place the path rule is applied — on both the write and
the read path.

nav_public therefore grew a { items, sections, links } wrapper. A bare map still
reads as the items map, and a nav with no sections still stores one, so this
changed nothing for a nav that does not use it. Free to do now because nothing
has shipped; after the cutover it would have needed a migration.

The Public tab gets its own editor. A public section is an entry in the
top-level order that the admin created and can drag among the pills, unlike the
admin sidebar's four coded sections, where only membership moves — that is a tree
rather than a list of groups. Deleting a section returns its entries to the top
level rather than removing them, which is the one destructive act this screen
could otherwise commit.

The dropdown opens on click and never on hover, and its trigger is not a link: a
hover menu is unusable on touch, and a trigger that navigates means tapping to
open takes you somewhere instead. Escape closes and returns focus, an outside
press closes, navigating closes, and Arrow Up/Down walk the items.

pruneNav applies the shard-feature gate inside a section and drops one it leaves
empty, so a dropdown never opens onto nothing.

Also fixes a bug this surfaced in the phase 6-8 code: the save path judged "does
this route still exist?" against the palette — the base array already filtered to
what the editing admin can see — so on the public header a feature-gated row's
override could never be carried through and would have been silently reset.
Membership is now judged against the full coded nav while the rows still come
from the palette.

Co-Authored-By: Claude <noreply@anthropic.com>

server/swagger/swagger-output.json

@@ -3463,7 +3463,7 @@
           "Admin · Settings"
         ],
         "summary": "Update site settings (admin only)",
-        "description": "Writes the given keys. The JSON-valued theming keys (theme_visual, brand_assets, nav_public, nav_admin, nav_player) accept an object or its stringified form, are validated strictly with the offending field named in the 400, and are stored stringified with unusable fields dropped. Nav overrides carry only label/order/hidden/group; whether a key names a route the nav declares is settled client-side at merge time.",
+        "description": "Writes the given keys. The JSON-valued theming keys (theme_visual, brand_assets, nav_public, nav_admin, nav_player) accept an object or its stringified form, are validated strictly with the offending field named in the 400, and are stored stringified with unusable fields dropped. Nav overrides key coded entries by their existing route and carry only label/order/hidden/group/section; whether a key names a route the nav declares is settled client-side at merge time. nav_public may additionally carry admin-created dropdown `sections` and admin-authored `links` — the only place an arbitrary path may be named, and therefore restricted to same-origin paths (no scheme, no protocol-relative host). Sections and links are dropped for the other two navs, which cannot render them.",
         "responses": {
           "200": {
             "description": "Updated settings",