docs: update readme to simplify and reflect docs refactor

Description

Updates the readme to streamline the content and link to the user docs published at docs.gitlab.com as the single source of truth. It also removes some links that are broken now that I've started refactoring the user docs.

Related Issues

• https://gitlab.com/gitlab-org/gitlab/-/work_items/585922+
• Docs: next steps for extension docs centralizat... (gitlab-org/editor-extensions/meta#282)

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