refactor: improve initialization error messages

[badosu]

See for example:

• Fails to initialize in neovim #273 (comment).

[ERROR][2025-12-20 12:11:21] ...lsp/handlers.lua:562 '[Project file:///path/to/project] Failed to initialize: {:shutdown, {:failed_to_start_child, {XPExpert.Project.Node, "project"}, {:error, :normal, ~c"could not compile dependency :elixir_sense, \"mix compile\" failed. Errors may have been logged above. You can recompile this dependency with \"mix deps.compile elixir_sense --force\", update it with \"mix deps.update elixir_sense\" or clean it with \"mix deps.clean elixir_sense\"\n"}}}'

• Failed to start on windows with zed #266

[Project file:///d%3A/proj/hello] Failed to initialize: {:shutdown, {:failed_to_start_child, {XPExpert.Project.Node, "hello"}, {:error, :normal, ~c"done\r\n"}}}

[doorgan]

Thank you! 💜