chore(integ-runner): use newStyleSynthesis by default

[corymhall]

This PR updates the integ-runner to not set @aws-cdk/core:newStyleStackSynthesis: false by default.
Previously this was done to cut down on the merge conflicts when the forward-merge was done
between v1 and v2, but since we are now only committing to v2 it makes sense to test with
newStyleStackSynthesis enabled.

This change required re-running all integration tests since using this flag changes the template. I've separated out some of the important changes into their own commits to make it easier to review.

• chore(integ-runner): use newStyleSynthesis by default - this contains the actual change to the integ-runner
• integ test shapshot updates - this contains the snapshot updates for most of the tests
• The commits that mention a specific module contain fixes for broken integration tests

---

All Submissions:

• Have you followed the guidelines in our Contributing guide?

Adding new Unconventional Dependencies:

• This PR adds new unconventional dependencies following the process described here

New Features

• Have you added the new feature to an integration test?
  • Did you use yarn integ to deploy the infrastructure and generate the snapshot (i.e. yarn integ without --dry-run)?

By submitting this pull request, I confirm that my contribution is made under the terms of the Apache-2.0 license

[gitpod-io]

[Naumel]

Realistically, my eyes might have glossed over a few changes.
Having gone through them commit by commit, I think it's as close to an in-depth review as humanly possible.

[mergify]

Thank you for contributing! Your pull request will be updated from main and then merged automatically (do not update manually, and be sure to allow changes to be pushed to your fork).

[aws-cdk-automation]

AWS CodeBuild CI Report

• CodeBuild project: AutoBuildv2Project1C6BFA3F-wQm2hXv2jqQv
• Commit ID: 0150e65
• Result: SUCCEEDED
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[mergify]

Thank you for contributing! Your pull request will be updated from main and then merged automatically (do not update manually, and be sure to allow changes to be pushed to your fork).