fix: remove Model ID field from public models in admin

Public models are now display-only and don't require a Model ID:
- Removed Model ID input field from admin.html public models section
- Updated admin.js to not require or send Model ID for public models
- Updated server API to accept public models without Model ID
  - Uses display label as the identifier for public models
  - Only requires Model ID for OpenCode models (which need it for execution)

Public models are purely for user-facing display in the builder dropdown,
while OpenCode models form the actual execution fallback chain.

chat/public/admin.html

@@ -120,10 +120,6 @@
         </header>
         <p style="margin-top:0; color: var(--muted);">These models are displayed to users in the builder dropdown for selection. This is separate from the OpenCode fallback chain.</p>
         <form id="public-model-form" class="admin-form">
-          <label>
-            Model ID (e.g., claude-3-5-sonnet, gpt-4o)
-            <input id="public-model-name" type="text" placeholder="Enter model ID manually" required />
-          </label>
           <label>
             Display name shown to users
             <input id="public-model-label" type="text" placeholder="Friendly label (e.g., Claude 3.5 Sonnet)" required />