feat: Dynamically load Google API client, remove gapi-script dependency, and mark sync settings as client-side.

package-lock.json

@@ -23,6 +23,7 @@
       },
       "devDependencies": {
         "@tailwindcss/postcss": "^4",
+        "@types/gapi.auth2": "^0.0.61",
         "@types/node": "^24",
         "@types/react": "^19",
         "@types/react-dom": "^19",
@@ -1620,6 +1621,16 @@
       "integrity": "sha512-/ZsLuq6BffMgbKMtZyDZ8vwQvTyKhKQ1G2K6VyWCgtHHhfSSXbk4+4JwImZiTjWNXfI2q1ZStAwFFHSkNoTkHA==",
       "license": "MIT"
     },
+    "node_modules/@types/gapi.auth2": {
+      "version": "0.0.61",
+      "resolved": "https://registry.npmjs.org/@types/gapi.auth2/-/gapi.auth2-0.0.61.tgz",
+      "integrity": "sha512-cn+omiRoE/LTxZncnVl1QhcLggOT0sJ8Yz9RXIsw5R2zLyRf+0o6kaZzJ/Gr3Sxz6i7J/+PbXAF8yeZipCaiWw==",
+      "dev": true,
+      "license": "MIT",
+      "dependencies": {
+        "@types/gapi": "*"
+      }
+    },
     "node_modules/@types/gapi.client": {
       "version": "1.0.8",
       "resolved": "https://registry.npmjs.org/@types/gapi.client/-/gapi.client-1.0.8.tgz",