Epic: Integrate public API's into VS Code

[loujaybee]

Context	Integrate the newly created workspace Authentication and workspace management API's #8512 into VS Code Desktop.
Owner	Product - @loujaybee / Tech - @akosyakov
Value	Enable Gitpod users to have a full desktop IDE experience which does not require the user to authenticate or navigate to Gitpod in the browser to start or manage workspaces
Acceptance Criteria	- Auth flow is replaced with the new authentication API endpoints
Complexities	- Work is dependent on API's introduced as part of #7900
Latest Update	28.04.2022 - Updated note about dependencies on public API's. We cannot start this epic until that work progresses further

Remaining

• Provide feedback on Public API developer experience
• Migrate to stable Public APIs
• Migrate all self-hosted users (old versions of Gitpod)
• Improve reliability of Public API (implement caching)
• Implement observability into VS Code clients (e.g. VS Code Desktop)

[stale]

This issue has been automatically marked as stale because it has not had recent activity. It will be closed if no further activity occurs. Thank you for your contributions.

[loujaybee]

• We intend to scope this down and exclude auth + token related APIs to simplify
• We should consider scoping this down to the current version (version 1 - experimental)

[loujaybee]

@akosyakov to either:

1. Re-scope this to integration into supervisor, not VS Code.
2. Create another epic for supervisor, and move this issue to the backlog.