ci: Do not allow web integration tests to fail

Description

This change makes the web integration tests stricter by requiring them to pass before allowing code to be merged. Previously, if these tests failed, the merge could still proceed, but now any test failures will block the merge until the issues are fixed.

Related Issues

Resolves #[issue_number]

How has this been tested?

• If src/browser or src/common has been modified, please consider interoperability with the Web IDE. See Running the Extension in WebIDE.
• Consider an end-to-end test for significant new features that aren't covered by integration tests.

Screenshots (if appropriate)

What CHANGELOG entry will this MR create?

• fix: Bug fix fixes - a user-facing issue in production - included in changelog
• feature: New feature - a user-facing change which adds functionality - included in changelog
• BREAKING CHANGE: (fix or feature that would cause existing functionality to change) - should bump major version, mentioned in the changelog
• None - other non-user-facing changes