☔ Migration to `package:unified_analytics` for analytics collection

[eliasyishak]

This serves as a tracker issue for the migration efforts for devtools to package:unified_analytics

Tasks:

• Setup the analytics instance and integrate the necessary APIs for onboarding a new user
  • [x] PR in flutter/devtools to add logic: https://github.com/flutter/devtools/pull/7084
  • [x] PR in dart-lang/tools to check legacy file: https://github.com/dart-lang/tools/pull/227
  • [x] PR in dart-lang/tools to fix behavior for showing message: https://github.com/dart-lang/tools/pull/228
  • [ ] [SWAP WITH PR] https://github.com/flutter/devtools/issues/7230

Migration for events

• [ ] Timing events
• [ ] Screen views
• [ ] Impressions
• [ ] Select (selecting tabs)