Diagnose Issues with Copilot

Create an entry point called "diagnose with copilot" that could be introduced as a button to different error messages which get surfaced to the user as part of this extension. With just a single click users could get help with their environment, package, dependency, etc problems. It would mirror the remote-ssh button with a similar name. The additional features this button would add is context, specific tools, output logs, and knowledge of common problems. Per @roblourens suggestion, I would like to design this using a custom chat mode. To do so, there are 2 updates needed to custom chat modes to make it work for this case:

1. The ability for an extension to send a chat message in a custom chat mode- ie starting up this chat mode with a message and no additional user interaction
2. This custom mode being transient. Currently custom modes are saved in a file format and live on in the users workspace. This doesn't make a ton of sense for this use-case because we anticipate people would face a problem setting up their workspace (environment, pkgs etc) and want help via this chat but once they are done, they wont need to return to it. With this is in mind we would love if it would be temporary, only lasting through that session or not being saved to their workspace. Curious your thoughts @roblourens on what this could look like / if this would be possible.

cc @cwebster-99 and @karthiknadig