I'm on Lunarvim and I can check the line diagnostic with gl.
But I don't know how to go there with the cursor and copy the text, the mouse doesn't work either.
It is likely that the diagnostic popup window is set to be non-focusable. So you can not move your cursor to the popup window and copy text. However, you can try command lua vim.diagnostic.setqflist(), which should populate your quickfix list with diagnostic and you can copy from there.