chore: use ssh private key for git sync

[trivikr]

Checklist

Internal JS-6078

Referred documentation https://github.com/wei/git-sync
Once this commit is merged, we'll verify that git-sync is successful.

On success, we'll delete the following:

• Secret: GIT_SYNC_SOURCE_REPO
• Secret: GIT_SYNC_SOURCE_SSH_PRIVATE_KEY
• Secret: GIT_SYNC_DESTINATION_SSH_PRIVATE_KEY
• Deploy key on this repo: git-sync-source-public-key
• Deploy key on destination repo: git-sync-destination-public-key

Similar change in v3 aws/aws-sdk-js-v3#7224

• npm run test passes
• .d.ts file is updated
• changelog is added, npm run add-change
• run bundle exec rake docs:api and inspect doc/latest/index.html if documentation is changed
• run npm run integration if integration test is changed
• non-code related change (markdown/git settings etc)

[trivikr]

Verified that git sync action is successful https://github.com/aws/aws-sdk-js/actions/runs/16486683527/job/46612674261
And the commit is synced to the destination repo.