Custom logging implementation could use VS Code's LSP APIs

Not really an issue, but just a refactoring suggestion.

I noticed that this repo has a custom logging implementation, but VS Code has a basically identical functionality already implemented here. There's no need to create extra output channels, since VS Code automatically creates one using the client's name.

An example where these LSP client methods are used can be found in the vscode-eslint extension. The output looks as follows:

If this sounds like a reasonable suggestion, I would gladly work on the refactoring :)

Start with editors/code/src/util.ts, especially the custom logging implementation linked in the issue. Compare it with the VS Code Language Server client logging methods and the vscode-eslint client example. Done means the existing logging behavior is refactored to use the relevant LSP client APIs without unnecessary extra output channels.