chore: Make GH workflows pass in staging & refactor using composite actions

[sichanyoo]

Issue #

1934

Description of changes

• Refactor workflows to re-use composite actions instead of having lots of duplicate steps.
• Adjusts CI workflow to make it work in staging repo as well.
• When the CI workflow runs in public smithy-swift repo and there is a corresponding branch in public aws-sdk-swift repo, it fetches that corresponding branch of public aws-sdk-swift to run tests.
• When the CI workflow runs in private smithy-swift repo and there is a corresponding branch in private aws-sdk-swift repo, it fetches that corresponding branch of private aws-sdk-swift to run tests.
• In both public and private situation, if there's no corresponding branch in respective partner repo, just the main branch is pulled to run tests.
• Tested using dummy PR in staging repo & confirmed all secrets are redacted in workflow logs as expected.

Scope

• Bug fix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)

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