docs(website): settle what core publishes about an installed module

Phase 2, PR 6 of MODULE_SYSTEM.md 2.7 — GET /api/v1/public/modules.

MODULE_API.md gains 2.9, the normative shape: four fields (id, name, version,
capabilities) in scan order, and what is deliberately absent. Only started
modules appear, so a disabled or failed one is absent exactly as 4.4 already
leaves its routes and nav; no state, failure_stage or failure_reason reaches an
anonymous caller; no client chunk URL, because htmlShell hands the browser the
tag; an empty array is a real answer, but the 7.6 guard is a 500 and never [].
Also records why it owns the /modules prefix rather than sitting in the
root-mounted site router, where the loader's collision probe could not see it.

6.7 amends MODULE_SYSTEM 2.6 step 4, which said the SPA reads the endpoint "to
learn what to load" — step 3 of the same list had already answered loading a
different way, and 3.1.3 is the normative version. The endpoint feature-detects.
2.6 step 4 now says so, and Part 6's intro no longer claims a fixed count of
amendments.

MODULE_SYSTEM.md 2.7 records PR 6 and restates the phase exit criterion
honestly: no EXISTING URL moves, and PR 6 is the single deliberate addition in
Phase 2. Status line updated — the design is in implementation, not unimplemented.

BACKEND_DESIGN.md documents the route in the /public table and the router in the
folder map, and the published api-route-inventory.json mirror is refreshed to
228 public routes (the prose count was stale at 226).

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

website/api-route-inventory.json

@@ -781,6 +781,10 @@
       "method": "POST",
       "path": "/api/v1/public/contact"
     },
+    {
+      "method": "GET",
+      "path": "/api/v1/public/modules"
+    },
     {
       "method": "GET",
       "path": "/api/v1/public/pages/:id/preview/:token"