ci: check web JavaScript syntax

[tunglambk]

Closes #174

Description

Adds a dedicated GitHub Actions workflow for changes under web/**. It runs node --check web/app.js, so JavaScript syntax errors block the pull request before they reach the GUI. The workflow also watches its own file so future gate changes are checked.

Local validation: node --check web/app.js, YAML parsing, and git diff --check.

Type of change

• Bug fix (non-breaking change that fixes an issue)
• New feature (non-breaking change that adds functionality)
• Breaking change (fix or feature that would change existing behavior)
• Documentation update
• Refactor / code cleanup
• Other: CI

Checklist

• I have tested my changes locally
• Shared extraction and download logic is unaffected
• I have kept the single-file architecture (no package split)
• I have not added new dependencies

Screenshots / logs (if applicable)

Not applicable.