[Feature Request] Status indicator for active compilation buffer

[Thaodan]

Is your feature request related to a problem? Please describe. The compilation buffer as no status indicator when it is running like the builtin mode line does.

Describe the solution you'd like An indicator about the compilation buffer to be active similar to the lsp indicator.

Describe alternatives you've considered Use some minor mode to show the status.

Additional context

• https://www.emacswiki.org/emacs/CompilationMode