Re-lands https://github.com/flutter/flutter/pull/137191.

The fix for the issue causing that PR to be reverted was tested in this PR but ultimately landed separately in https://github.com/flutter/flutter/pull/138093.

Reverts flutter/flutter#137191
Initiated by: camsim99
This change reverts the following previous change:
Original Description:
Adds support for Android 34 in the following ways:

- Bumps integration tests compile SDK versions 33 --> 34
- Bumps template compile SDK version 33 --> 34
- Also changes deprecated `compileSdkVersion` to `compileSdk`

Part of https://github.com/flutter/flutter/issues/134220

Adds support for Android 34 in the following ways:

- Bumps integration tests compile SDK versions 33 --> 34
- Bumps template compile SDK version 33 --> 34
- Also changes deprecated `compileSdkVersion` to `compileSdk`

Part of https://github.com/flutter/flutter/issues/134220

I'm removing an unneded block of configuration from the `settings.gradle` template. It was introduced by me in #123511. At that time, I did not know that it's unnecessary, and did not test removing it – sorry about that.

I learned that it's unnecessary recently, when [I asked a question on StackOverflow](https://stackoverflow.com/questions/77073596/whats-the-difference-between-plugins-and-pluginmanagement-plugins-in). More context there.

Reverts flutter/flutter#137190

I'm seeing these in the bot reports every week. Hopefully this is all of
them, and hopefully 4GB is enough.

The skeleton id needed to be updated to be sent to app store or play store

This app will be use for a11y assessments. See [design doc](http://go/flutter-gar-reporting-q3-2023)    (internal only)