Use Web IDE AuthProvider instead of mediator commands

• Epic: Enable Web IDE Extension Marketplace for GitLab... (&11769 - closed)
• Use Web IDE AuthProvider instead of mediator co... (#1253 - closed)
• Move mediator commands into vscode-extension-we... (gitlab-web-ide#310 - closed)

Description

When the gitlab-web-ide authentication provider is available, let's use that to

Plan

1. Refactor current GitLab client from desktop/ to browser/
2. Use this new client for fetchFromApi implementation in browser/ when the gitlab-web-ide authentication exists

Please note: Until the web_ide_oauth feature flag is removed, we need to still support the possibility of mediator commands. Please see gitlab#433324 (closed) for status on this flag.