copilot: Use latest Copilot API spec

[imumesh18]

Recently we started to use the new copilot-lsp which has different spec compare to the copilot.vim and it returns a lot of warnings for using the older spec. This PR upgrades it to use the latest spec.

Logs

2025-05-07T21:07:24-03:00 INFO  [lsp] Language server with id 0 sent unhandled notification window/logMessage:
{
  "type": 2,
  "message": "[sdk] setEditorInfo is deprecated. Use initializationOptions for editorInfo and editorPluginInfo and workspace/didChangeConfiguration for editorConfiguration."
}

New Docs: https://github.com/github/copilot-language-server-release/blob/main/README.md

• Replace SignInInitiate with SignIn request and update related types
• Move editor info into InitializationOptions and remove SetEditorInfo request

Release Notes:

• N/A