How do I repeat any command in Vim, like “C-x z” in emacs?

To repeat a command-line command, try @:, To repeat a normal/insert-mode command, try .,

Add below mapping to your .vimrc if you want to shortcut the same:-

:noremap <C-P> @:<CR> – This will map Ctrl+P to previous command-line command. You can map any other combo.