[APP-1782] Migrate to new analytics APIs (#9735)

* Migrate logEvent to useAnalytics

* Migrate logger.metric to useAnalytics

* Migrate tricky spot, fix types

* Migrate remaining tricky spot

* Missed one

* Remove metric() from logger

* Migrate useGate to useAnalytics

* Remove all other StatSig mentions

* Update event payload

* Update logger tests

* Mock expo method

package.json

@@ -220,7 +220,6 @@
     "react-textarea-autosize": "^8.5.3",
     "sonner": "^2.0.7",
     "sonner-native": "^0.21.0",
-    "statsig-react-native-expo": "^4.6.1",
     "tippy.js": "^6.3.7",
     "tlds": "^1.234.0",
     "tldts": "^6.1.46",