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 />

chat/public/admin.js

@@ -34,7 +34,6 @@
     opencodeModelsCount: document.getElementById('opencode-models-count'),
     // Public Models (user-facing selection)
     publicModelForm: document.getElementById('public-model-form'),
-    publicModelName: document.getElementById('public-model-name'),
     publicModelLabel: document.getElementById('public-model-label'),
     publicModelTier: document.getElementById('public-model-tier'),
     publicModelIcon: document.getElementById('public-model-icon'),
@@ -2425,16 +2424,11 @@
   if (el.publicModelForm) {
     el.publicModelForm.addEventListener('submit', async (e) => {
       e.preventDefault();
-      const name = el.publicModelName.value.trim();
       const label = el.publicModelLabel.value.trim();
       const icon = el.publicModelIcon ? el.publicModelIcon.value : '';
       const tier = el.publicModelTier ? el.publicModelTier.value : 'free';
       const supportsMedia = el.publicModelMedia ? el.publicModelMedia.checked : false;
       
-      if (!name) {
-        setPublicModelStatus('Model ID is required.', true);
-        return;
-      }
       if (!label) {
         setPublicModelStatus('Display name is required.', true);
         return;
@@ -2446,7 +2440,6 @@
           method: 'POST',
           body: JSON.stringify({ 
             type: 'public',
-            name, 
             label, 
             icon, 
             tier, 
@@ -2454,7 +2447,6 @@
           }),
         });
         setPublicModelStatus('Saved');
-        el.publicModelName.value = '';
         el.publicModelLabel.value = '';
         await loadConfigured();
       } catch (err) {