feat: Use Language Server for code suggestions in web ide

Description

This Merge Request ensures that the web build of the GitLab VSCode Extension can use the Language Server to provide Code Suggestions in the Web IDE. It identifies all the configuration gaps and fix them.

Related Issues

[VSCode] Use Language Server to serve code sugg... (#2083 - closed)

How has this been tested?

1. On the terminal, access the web ide project and run yarn start:example.
2. On a separate terminal tab, access the GitLab VSCode Extension project, checkout this branch, and run npm run watch:browser.
3. Open the Web IDE and fill the configuration parameters. I tested these changes pointing to gitlab.com because my GDK is very unreliable at serving code completion.
4. Open a file with a file type supported by Code Suggestions. Try getting code suggestions. It should work without any problems.
5. Duo Chat should also work as usual.

• 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)

code_suggestions_web_ide_demo_1080p.mov

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