feat: Setup posthog analytics (#12291)

- Replace June.so analytics with PostHog integration
- Maintain existing analytics API interface for seamless migration
- Remove all the June references

_June.so is shutting down their service, requiring migration to an
alternative analytics provider. PostHog was chosen as the replacement
due to its robust feature set and similar API structure._

package.json

@@ -40,7 +40,6 @@
     "@hcaptcha/vue3-hcaptcha": "^1.3.0",
     "@highlightjs/vue-plugin": "^2.1.0",
     "@iconify-json/material-symbols": "^1.2.10",
-    "@june-so/analytics-next": "^2.0.0",
     "@lk77/vue3-color": "^3.0.6",
     "@radix-ui/colors": "^3.0.0",
     "@rails/actioncable": "6.1.3",
@@ -80,6 +79,7 @@
     "md5": "^2.3.0",
     "mitt": "^3.0.1",
     "opus-recorder": "^8.0.5",
+    "posthog-js": "^1.260.2",
     "semver": "7.6.3",
     "snakecase-keys": "^8.0.1",
     "timezone-phone-codes": "^0.0.2",