Improve consistency in client-side logout experience

[stirby]

Problem Statement

As of today, it's confusing when a coder user is logged out of a connected VScode window. When a user is connected to multiple workspaces, each window may show different behavior after logout.

One VSCode window might let you know that you signed out and that you need to re-login. Another will become unusable and disconnected, even after re-auth'ing Coder. The user must then close and reopen it. Another account had the user try to update their workspace from Coder's 'update' button in VSCode, but Coder was already logged out, so they got a 401 error.

Proposal

To reduce confusion, we should provide a consistent experience across all windows when the user is signed out. Communicating early and clearly that the user is no longer authenticated. The user should be prompted to re-authenticate when this advisory is presented.