Improve logging capabilities

In previous versions of the Flutter IntelliJ plugin, users had the option to enables an experimental log view "Flutter Logging".

While not perfect, this feature brought significant improvements for working with logs generated by the user's running Flutter app.

Notably, logs emitted by the app were categorized and color-coded with labels making it easy to differentiate and track messages. Basic filtering and error types were also great features to have.

In recent updates, this was removed from IntelliJ and added to Flutter's "Dev Tools". While this is a welcome improvement to the dev tools platform, it leaves users of IntelliJ (and vscode) with very basic, unfiltered logging requiring users to switch from their primary IDE to an external tool for very basic functionality.

Is it possible to add this feature back or at least enable some sort of filtering?

ref: https://github.com/flutter/flutter-intellij/pull/4005

cc: @RedBrogdon @devoncarew

Start by reviewing the referenced Flutter IntelliJ PR #4005 and the current issue discussion to understand what the former Flutter Logging view provided. Define whether the intended outcome is restoring that view or adding narrower log filtering; completion should specify the supported logging capabilities and their IntelliJ behavior.

Written by the indexing model from the issue text.