chore: Drop unused files from aws/karpenter-provider-aws repo

[jonathan-innis]

Fixes #N/A

Description

This drops the following sets of files from the repo:

1. Publish Test Tools Workflow - This workflow was used for pushing an updated docker image when we were using Tekton for our E2E testing. We have since dropped support for Tekton; so, we can remove these files from the repo
2. Provisioner Examples - These examples should have been dropped at the v1alpha5 migration on v0.33.x. These examples still exist on older tagged versions of the repo but shouldn't exist on the latest version
3. Sync Cluster - These scripts were artifacts of the old SQS-based Tekton workflows. These have since been replaced
4. Dockerfile and push-docker.sh - This script was used in the Publish Test Tools workflow that was mentioned earlier for pushing newer versions of the testing image up to our test ECR for Tekton.

How was this change tested?

Does this change impact docs?

• Yes, PR includes docs updates
• Yes, issue opened: #
• No

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

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[coveralls]

Pull Request Test Coverage Report for Build 7189876908

• 0 of 0 changed or added relevant lines in 0 files are covered.
• No unchanged relevant lines lost coverage.
• Overall coverage remained the same at 82.489%

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Totals
Change from base Build 7189741306:	0.0%
Covered Lines:	4918
Relevant Lines:	5962

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💛 - Coveralls