feat: use git-sync action to sync with private mirror

[trivikr]

Issue #, if available:
Similar to aws/aws-sdk-js-v3#1965

Description of changes:
use git-sync action to sync with private mirror

Testing:
Testing done with the following packages:

• source: trivikr/git-sync-test
• destination: trivikr/private-git-sync-test

Config tested: https://github.com/trivikr/git-sync-test/blob/302d7d5cf429594757c9a32ead5e0816715f9b95/.github/workflows/git-sync.yml
Example GitHub Action run: https://github.com/trivikr/git-sync-test/runs/1778705960?check_suite_focus=true

Verified that secrets are not shown in the GitHub Action log

GitHub Action log

Cloning into '/root/source'...
[email protected]:***.git:main
[email protected]:***.git:main
Warning: Permanently added 'github.com,140.82.113.3' (RSA) to the list of known hosts.
* main                302d7d5 [source/main] chore: update step name to git-sync
  remotes/source/HEAD -> source/main
  remotes/source/main 302d7d5 chore: update step name to git-sync
Warning: Permanently added the RSA host key for IP address '140.82.114.4' to the list of known hosts.
To github.com:***.git
   de881a8..302d7d5  main -> main

Note that:

• source GitHub URL is hidden [email protected]:***.git:main
• destination GitHub URL is hidden [email protected]:***.git:main
• destination GitHub URL is hidden in git output To github.com:***.git

By submitting this pull request, I confirm that you can use, modify, copy, and redistribute this contribution, under the terms of your choice.

[trivikr]

Values populated in GitHub repositories:

• Source repo awslabs/smithy-typescript
  • secrets.GIT_SYNC_SOURCE_REPO
  • secrets.GIT_SYNC_DESTINATION_REPO
  • secrets.GIT_SYNC_SOURCE_SSH_PRIVATE_KEY
  • secrets.GIT_SYNC_DESTINATION_SSH_PRIVATE_KEY
  • deploy public key for secrets.GIT_SYNC_SOURCE_SSH_PRIVATE_KEY
• Destination repo **private**
  • deploy public key for secrets.GIT_SYNC_DESTINATION_SSH_PRIVATE_KEY

[trivikr]

Verified that git-sync run was successful.
GitHub Action run: https://github.com/awslabs/smithy-typescript/runs/3604393420

Verified that force-push was successful on the main branch of private mirror.