Option to show source in diagnostic picker

Is your feature request related to a problem? Please describe. When there's multiple servers attached, and opening diagnostics picker, I don't know which diagnostic is coming from which server.

Describe the solution you'd like Add option to diagnostic picker to show source.

Describe alternatives you've considered

Additional context There's issue #2110 that proposes to directly append the source to diagnostic message, but I think it's better to add it as an option