Fixes https://github.com/flutter/flutter/issues/123172
Fixes https://github.com/dart-lang/sdk/issues/51813

In combination with https://github.com/flutter/flutter/pull/136418.

Enable prefer_mixin

* dart fix --apply

* manual fixes

* fix after merge conflicts

* review

This adds avoid_dynamic_calls to the list of lints, and fixes all instances where it was violated.

Importantly, this lint is NOT turned on for flutter/packages/test, because those changes are happening in another PR: #84478