ci: Run Web IDE integration tests in pipeline

Description

It sets up a CI job that runs the Web IDE's code suggestions integration tests in the GitLab VSCode Extension project using the browser build of the extension based on the Merge Request's branch. This job will help us prevent regressions in the Web IDE by providing feedback early in the extension development lifecycle.

Related Issues

[VSCode] Run Web IDE code suggestions test in t... (#2115 - closed)

How has this been tested?

The following pipeline's output demonstrates that the CI job builds the Web IDE using the browser build of the VSCode Extension generated in the same job https://gitlab.com/gitlab-org/gitlab-vscode-extension/-/jobs/11475090743#L596

• 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