Check and fix workflow builds

[Pterjudin]

Fixes GitHub Actions workflows to ensure correct branch checkout and proper metadata propagation between jobs.

Previously, actions/checkout could fail due to a blank ref, and downstream compile/package jobs were short-circuiting because they weren't receiving the computed metadata (like MS_COMMIT, SHOULD_BUILD) from the check job. This PR addresses both issues by explicitly setting GITHUB_BRANCH and correctly exporting and consuming job outputs.

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[cursor]

Cursor Agent can help with this pull request. Just @cursor in comments and I'll start working on changes in this branch.
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