feat: 구글 로그인/가입 — 웹(GIS)·앱(네이티브 Credential Manager)

- LoginModal: 서버에서 구글 클라이언트 ID 수신 시에만 버튼 노출
  - 웹/PC: Google Identity Services 렌더 버튼
  - 앱(안드로이드): @capawesome/capacitor-google-sign-in 네이티브 버튼
- 네이티브/웹 모두 ID 토큰을 /api/auth/google 로 전달(aud=웹 클라이언트 ID)
- auth 스토어/authApi 에 googleLogin·googleClientId 추가
- src/native/googleAuth.js 네이티브 래퍼 신규

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

package-lock.json

@@ -14,6 +14,7 @@
         "@capacitor/cli": "^8.3.4",
         "@capacitor/core": "^8.3.4",
         "@capacitor/preferences": "^8.0.1",
+        "@capawesome/capacitor-google-sign-in": "^0.1.2",
         "@toast-ui/editor": "^3.2.2",
         "@toast-ui/editor-plugin-code-syntax-highlight": "^3.1.0",
         "axios": "^1.16.1",
@@ -1195,6 +1196,25 @@
         "@capacitor/core": ">=8.0.0"
       }
     },
+    "node_modules/@capawesome/capacitor-google-sign-in": {
+      "version": "0.1.2",
+      "resolved": "https://registry.npmjs.org/@capawesome/capacitor-google-sign-in/-/capacitor-google-sign-in-0.1.2.tgz",
+      "integrity": "sha512-41Z5LBVZJQ/20lEbzQJUtjfm7rCUhiq0EsfKmytTfKjqUjQB4zy0zlDMowe/z5CtetL8u7WGvERtyRYil2exww==",
+      "funding": [
+        {
+          "type": "github",
+          "url": "https://github.com/sponsors/capawesome-team/"
+        },
+        {
+          "type": "opencollective",
+          "url": "https://opencollective.com/capawesome"
+        }
+      ],
+      "license": "MIT",
+      "peerDependencies": {
+        "@capacitor/core": ">=8.0.0"
+      }
+    },
     "node_modules/@cspotcode/source-map-support": {
       "version": "0.8.1",
       "resolved": "https://registry.npmjs.org/@cspotcode/source-map-support/-/source-map-support-0.8.1.tgz",