Blocked by lack of clarity in requirements. Is waiting for response.

This is a subtask of #4879

It's a follow-up of #4881. While the previous subtask just fixes the user problem with minimal changes, here we can make further improvements. By separating this tasks we:

• make changes more atomic and easier to test and review
• can provide the bugfix faster with the previous issue
• have more room to discuss improvements in the current issue

Description

Every time GitHubGitProvider calls directly to getBuiltInIntegrationSession() and sometimes these requests are not silent. As a result, this option appear:

Questions

1. Do we want to prevent it by making GitHubGitProvider to call to the GitHubAuthenticationProvider rather than to VSCode session directly? (No)
   1. Do we want to detect that we want with local file systems and do not call the authentication requests when we do not need to read remotely? (?)
2. Now GitHubGitProvider never uses Cloud session. If I open on Web and authenticate in GKDev it shows me PRs on the launchpad but does not show a Blame, because GitHubGitProvider works with the local session
   
   Do we want to use Cloud session for file-system features?
3. Vice versa: do we want keep using local session (when it's available) for cloud features such as Launchpad and others?
4. If answer to above is YES, do we want to improve usage?
   1. now it's used when a cloud session is not available, but the local session is available
   2. we could, for example, when see that user is on cloud, flag it in state and when it's flagged, never try to use local sessions again. But while it's not flagged, that means that we never used cloud, so we can try to keep using locals.