docs: move model catalog out of shared

The model catalog is no longer a frontend/backend runtime contract.

Keeping it under shared made ownership misleading. It implied the catalog was
application code shared by runtime consumers, even though it now only supports
README links and public API documentation.

Move the catalog into public so it lives beside the docs surfaces that need it.
This gives the API docs a stable, served module and gives README readers a
linkable source without suggesting frontend or backend runtime dependency.

Render the API docs model list from the exported provider registry instead of a
hardcoded Claude/Cursor/Codex subset. That keeps Gemini and OpenCode visible and
makes future provider documentation changes flow through one docs-specific file.

Update README links, provider maintenance notes, and package files so published
artifacts include the standalone docs page and model catalog without relying on
the old shared path.

package.json

@@ -10,6 +10,8 @@
   "files": [
     "server/",
     "shared/",
+    "public/api-docs.html",
+    "public/modelConstants.js",
     "dist/",
     "dist-server/",
     "scripts/",