fix: resolve ProviderModelNotFoundError on non-Claude runtimes (#1156)

Extend resolve_model_ids to accept "omit" value: returns empty string
so non-Claude runtimes (OpenCode, Codex, Gemini, etc.) use their
configured default model instead of unresolvable Claude aliases.

- resolve_model_ids: "omit" short-circuits before alias resolution
- model_overrides still respected (checked first) for explicit IDs
- Installer sets resolve_model_ids: "omit" in ~/.gsd/defaults.json
  for non-Claude runtimes during install
- 4 new tests covering omit behavior and override passthrough
- Fix websearch test mocks for fs.writeSync output change (#1276)

Closes #1156

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

tests/core.test.cjs

@@ -281,6 +281,31 @@ describe('resolveModelInternal', () => {
       assert.strictEqual(resolveModelInternal(tmpDir, 'gsd-planner'), 'opus');
     });
   });
+
+  describe('resolve_model_ids: "omit"', () => {
+    test('returns empty string for known agents', () => {
+      writeConfig({ resolve_model_ids: 'omit' });
+      assert.strictEqual(resolveModelInternal(tmpDir, 'gsd-planner'), '');
+    });
+
+    test('returns empty string for unknown agents', () => {
+      writeConfig({ resolve_model_ids: 'omit' });
+      assert.strictEqual(resolveModelInternal(tmpDir, 'gsd-nonexistent'), '');
+    });
+
+    test('still respects model_overrides even when omit', () => {
+      writeConfig({
+        resolve_model_ids: 'omit',
+        model_overrides: { 'gsd-planner': 'openai/gpt-5.4' },
+      });
+      assert.strictEqual(resolveModelInternal(tmpDir, 'gsd-planner'), 'openai/gpt-5.4');
+    });
+
+    test('returns empty string with inherit profile', () => {
+      writeConfig({ resolve_model_ids: 'omit', model_profile: 'inherit' });
+      assert.strictEqual(resolveModelInternal(tmpDir, 'gsd-planner'), '');
+    });
+  });
 });
 
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