fix(model-config): keep model selection valid and fix admin panel edge cases

- Fall back to the default server model when a saved one disappears
- Sync model config across tabs
- Validation uses the base path and sends the access code
- Model ids edited as drafts (no empty, duplicate or padded ids)
- Credential changes reset validation; stale validation results are dropped
- Admin: generateId over HTTP, env-locked group switches, discard and toggle fixes,
  clearing a secret field keeps the saved key, first provider not auto-default when .env sets AI_MODEL
- Model selector items use unique values

components/model-selector.tsx

@@ -264,9 +264,13 @@ export function ModelSelector({
                                                         (model) => (
                                                             <ModelSelectorItem
                                                                 key={model.id}
-                                                                value={
-                                                                    model.modelId
-                                                                }
+                                                                // Unique value so same-named models highlight
+                                                                // separately; keywords keep search by name
+                                                                value={model.id}
+                                                                keywords={[
+                                                                    model.modelId,
+                                                                    providerLabel,
+                                                                ]}
                                                                 onSelect={() =>
                                                                     handleSelect(
                                                                         model.id,
@@ -351,9 +355,11 @@ export function ModelSelector({
                                                         (model) => (
                                                             <ModelSelectorItem
                                                                 key={model.id}
-                                                                value={
-                                                                    model.modelId
-                                                                }
+                                                                value={model.id}
+                                                                keywords={[
+                                                                    model.modelId,
+                                                                    providerLabel,
+                                                                ]}
                                                                 onSelect={() =>
                                                                     handleSelect(
                                                                         model.id,