Internal: Update publish script [TMZ-803]

[hein-obox]

✨ PR Description

Purpose: Refactor WordPress.org theme deployment workflow by removing dry-run mode and streamlining SVN operations for more reliable production publishing.

Main changes:

• Removed dry-run workflow input and separate dry-run shell script to simplify deployment process
• Moved SVN credential validation after file operations to prevent early authentication failures
• Enhanced SVN operations by adding explicit delete command for removed files and improved status filtering

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