Add dry-run testing for crate publishing workflow

[Copilot]

The automated publish workflow could only be triggered by pushing version tags, making it impossible to test changes to the workflow or validate a release without actually publishing to crates.io.

Changes

Workflow trigger

• Added workflow_dispatch with dry_run input (defaults to true)
• Skip tag version validation when manually triggered

Publish logic

• Pass --dry-run flag to cargo publish when enabled
• Skip crate availability polling in dry-run mode (no actual uploads)
• Visual indicators for mode: 🧪 DRY-RUN MODE vs 📦 LIVE MODE

Documentation

• RELEASING.md: Testing section with dry-run vs live comparison
• .github/TESTING_RELEASES.md: Step-by-step testing guide

Usage

Manual test without publishing:

# GitHub Actions UI → "Publish to crates.io" → "Run workflow"
# Branch: main, dry_run: true

Actual publish (unchanged):

git tag v0.46.0 && git push origin v0.46.0

Dry-run validates packaging, dependencies, and publish order across all 15 crates without uploading to the registry.

Original prompt

---

This section details on the original issue you should resolve

<issue_title>Automate crate publishing</issue_title>
<issue_description>## Is your feature request related to a problem? Please describe.
Automatically publish new versions to crates.io</issue_description>

Comments on the Issue (you are @copilot in this section)

• Fixes Automate crate publishing #752

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